It's a bit of a cliché, but it's true. The longer any given conversation in Britain (or Ireland), the higher the chance that the weather will be mentioned at some point.
This is because it's so varied. It is not uncommon to have all four seasons in a single day.
A big factor in this is prevailing winds: the British Isles have the Gulf Stream/North Atlantic Drift from the south west, which prevents the countries from getting Canada/Nordic-level cold (same latitude), but also brings storms. There's also cold winds from the north.
But the main reason is that the British are chronically shy and use the weather as a conversational totem, allowing conversation and agreement between strangers, without having to potentially invade their personal space (as described by Kate Fox in her book Watching the English). The most fundamental rule of 'weatherspeak' is to agree with the first speaker, even if you then immediately qualify it in such a way as indicates the opposite, eg, 'It's too hot today', 'yeah, it is, but I don't mind it myself'. Also it is often the only "safe" topic for any given two strangers to talk about and not risk some sort of argument. In the UK everything is Serious Business to someone. It's been said that the British have only two hobbies, complaining about the weather, and arguing.
Britain tends to have three seasons - a cold season, a wet season, and a cold and wet season. John Cleese once told David Letterman, "We have a national holiday. It's called summer", and there was more truth in that than most people realise - the default settings of British weather are, as noted, cold and wet, and if you're lucky, there may be a week or so of sunshine between the latter two. The latter leads to the famous 'cricket and strawberries' weather, and the famous English summer. However, it must also be borne in mind that in Britain, more or less anything over 14 degrees Celsius (57/58 Fahrenheit) is considered to be comfortable verging on warm, and anything over 20 degrees is hot. Bill Bryson noted seeing a forecast of 'Warm and dry, with cooler and rainy spells' and commentated that it could be printed every day, and in fact might be for all he knew, and hardly ever be wrong, and that unless you decide to go hiking up Ben Nevis in your dressing gown, you can probably get away with wearing the same thing all year round. Provided it comes with a hood or you're carrying your umbrella.
In seriousness, the British Isles are a temperate region, if a particularly damp one. Breaking the 30 degrees Celsius level occurs once or twice a year and 40 is unheard of (the UK record is 38.5 degrees in Kent in 2003). If it gets hot, expect at least one paper to have photographs of bikini-clad sunbathers — guaranteed. If it gets over 35 degrees, expect the tabloids to start pumping out horror stories about heat stroke, cancer threat from UV rays, and how the entire country is going to melt and/or die of thirst in a Biblical scale drought. Australians talking to British friends about the weather need to add "Celsius" after mentioning that their current temperature is about 45.
On the flip-side, very cold winters are also rare. British Christmas cards, decorations, and illustrations of pretty much any Christmas before the present day will usually have picturesque depictions of snow, sufficient to make snowmen of adequate size. In reality, heavy snow is particularly rare (snow of any sort is almost non-existent in cities outside of Scotland, and it's pretty scarce there too) and only occurs once or twice a year. Icy roads are a more common problem, with associated light snow. If it actually snows in any significant amount, expect most of the country (particularly the railways and the urban bits) to grind to a halt. In this context 'any significant amount' is more than about an inch and a half and there will inevitably be wall-to-wall news coverage. It says a lot about the British relationship with snow that whenever it snows in Doctor Who, there's generally an alien involved, and they're usually up to no good. And it's rarely actually snow. However, over the past few years, Britain has seen an increase in the amount of snow fall, and the amount of time it has settled for. It has been so severe that in 2010 entire stretches of motorways were blocked for days, schools were shut across the entire country and Britain encountered its coldest winter for 30 years. Older folk will often remember much bigger snowfalls When I Was Your Age..., but this may be due to the Nostalgia Filter - although while it will vary depending on where you were, the winters of 1947 and 1963 (both notoriously cold and snowy) and 1978-9, 1981-2 and 1991 were all memorably bad.
The most obvious thing anyone notices, however, is the rain. Virtually every day, somewhere will have a downpour. If you look at the weather forecast for Wales - which is the most proverbially and persistently damp part of Britain - on any given day, it predicts rain. The East Coast is supposed to be drier, but even there it's not exactly dry. Get two or three days of hot weather and a thunderstorm will generally finish it off. Wimbledon is a case in point, and rain (or bad light) is a frequent play-stopper in cricket. Football, on the other hand... only if the pitch is too frozen to play on, or actually flooded note , is a match called off. Rugby won't be called off for anything less than a direct meteor strike — and then, only for long enough to prop the posts back up, remove the meteorite, and patch up the poor sod it landed on. Glasgow is the rainiest city in the UK by average rainfall. This is not news to anyone who lives there, though it is a bit of a surprise to the inhabitants of Cardiff. British people are perversely proud of their rain. A vigorous debate arose on Facebook when a native Hawaiian posted that they lived in the rainiest place on Earth - a Hawaiian island that had had rain for 247 straight days. Readers were invited to top that. British readers obliged in droves. One correspondent from North Wales said "247 days? that's a drought!" Others pointed to their own native areas with pride and provided similar anecdotes suggesting Hawai'i was an underperforming amateur.
Floods were more common once upon a time, and still happen on occasions, especially in the Midlands and South West. However, matters like the draining of the frequently flooded Fens in East Anglia in the 19th and 20th centuries (there was an attempt in the 17th century, which failed miserably), and modern measures have prevented this in most of the country. London, for example, is protected by the Thames Barrier (that thing with three sails near London City airport), although that's more against very high tides.
Despite this, the Weather Agencies will insist that there is a drought on and the hosepipe ban will still be in effect. Naturally, everyone then goes about ignoring it, knowing that the next month will inevitably be spent chucking it down with rain. Some jokingly believe that the Weather Agency intentionally gives this warning simply to make the Gods angry. note
Wind can get pretty high, but the sea is too cold for hurricanes. We've had some close ones though. The Great Storm of 1987 is infamous, partly because of a weather forecaster named Michael Fish, who explained that there wasn't a hurricane on the way. He was technically correct - hurricanes occur by definition in the tropics - but there were definitely some hurricane-force winds, and no one has ever let him forget it. Actual hurricanes originally from the tropics (or at least subtropics) actually do occasionally make their way to Britain; 1986's Hurricane Charley, which famously caused massive amounts of very expensive damage in North Carolina and Virginia, actually managed to cross the Atlantic to dump historic amounts of rain on Ireland, Wales, and England, costing millions of pounds and killing eleven people. In the event of a storm, expect at least one picture of some brave/stupid (opinions may vary) souls braving crashing waves on a seashore, and usually in Cornwall, some enterprising/very stupid (opinions, again, may vary) souls trying to take advantage of the larger waves to surf. A favourite pastime of schoolchildren on a windy day is to lift their jacket up over their heads and walk into the wind. This is much more fun than it sounds.
The UK also has a surprisingly high amount of tornadoes, having the highest number of reported tornadoes compared to land mass of any country (and this includes Scotland and Northern England where they are very rare). These are rarely anything like as strong as those in the US's Tornado Alley, and are less common.
Pack an umbrella and a rain coat, that's all we can say. In the words of the Prophet Connolly, "There is no bad weather, only bad clothing".
In fiction, London, of course, will always have fog at some point of the story. In addition to natural fog, the burning of coal creates a lot of problems. In 1952 it is estimated that over 12,000 people died from four days of bad smog. Actual London, and indeed Britain in general, are today far less burdened with fog than some fictional works would have you believe, but their depictions can be given a bit more credence if set after industrialisation but before the passing of the clean air acts - though London today is still reliably a couple of degrees Celsius warmer than the rest of the country thanks to pollution and the urban heat island effect. Narrow river valleys Oop North are prone to mist and fog in winter, but it's rarely a London phenomenon nowadays. It's also not uncommon to see thick haar or 'sea fog' in coastal cities such as Edinburgh, but it isn't an everyday occurrence. See also A Foggy Day in London Town.
Irish weather is like British weather, but worse (although not as cold as Scotland). Indeed, the main reason that the lovely English cricket 'n' strawberries summer exists is that Ireland absorbs the worst of the rain that comes in from the Atlantic.
It's worth noting that British (and Irish) weather is actually far more temperate than it 'should' be, due to the Gulf Stream, and this is sometimes pointed out by commentators. Without the Gulf Stream, the British Isles would have a similar climate to Winnipeg, which is at the same latitude as the Isle of Wight. On the other hand however, Canada is colder than it should be as well, due to no natural barriers to the cold arctic winds straight from the North Pole. The warming effect of the Gulf Stream allows tropical plants to flourish in Wales and on occasion be grown as far north as Scotland.
One aspect of British and Irish weather that's often overlooked by writers used to lower latitudes is that the days are very long in the summer and very short in the winter - and sometimes, the Northern Lights can be seen in Scotland and its northern islands. This is especially the case in northern Scotland, but is true of the UK and Ireland in general. There's no "midnight sun" like in the polar regions, but 10 pm sun can be expected in midsummer, while it can start getting dim at something like 3PM in deep winter. It reaches the point that from Edinburgh northwards, Astronomical and Nautical Twilight essentially covers the entire night in June. The sun generally starts rising again sometime before 4AM in the summer, and as late as 08:45 in mid-winter. This has led to some degree of Fantastic Religious Weirdness here on Earth: Britain's substantial Muslim community, and particularly those living in Scotland,note have received numerous fatwas saying, "No, you don't have to fast from literal sunrise to sunset, seeing as that's a 15 or even 20-hour fast for 30 days when Ramadan falls in the summertime. 6 in the morning to 6 at night is just fine." With typical Scottish stubbornness, a lot of them do it anyway.
Notably April, most notorious for "April showers", is often the month when the Sun is first seen each year, often causing hill fires (identical to Australian bush fires, but on hills) and burning people who keep their liquid fuel cans outside then pick them up (honestly).note In 2012 there was a section of the North Midlands in drought and flood at the same time; this was not called "The Wettest Drought On Record" for no reason. In the North of England one week of blizzards and -13°C was followed by a week of heatwaves and +32°C. The Calder Valley flooded four times in three weeks later that year. In 2012 The Midlands experienced hailstones in July.
At any point in any season the country can, and will, endure just about every weather phenomena recorded. Electrical storms do occur, but are mild by the standards of other parts of the world. Earthquakes (which are not a weather phenomenon), or at least, ones that people actually notice, are extremely rare, as there have been no active faults in this particular bit of crust for hundreds of millions of years; when one does happen it is likely to take over the news for a few days.
In other words, there's a reason "The weather in London" used to be a meme on The Other Wiki.