: The family in Series 1 Episode 3 dies from the virus soon after leaving their home.
Just because they're running short of drinkable water doesn't mean there isn't enough around for washing (it is rainy old Britain after all, it's not like we're short of the stuff). And on their foraging expeditions, it's possible they brought back toiletries and whatnot both for hygiene purposes and to maintain some semblance of normality. But when all the soap, shampoo and makeup has run out and the last of the razor heads has blunted, they might look a little more grubby. In the series, it's too early for that, yet.
The reason the first series more resembles a Cozy Catastrophe
than the second...
...might well be because people back in the 1970s were more likely to have the hands-on practical skills and general resourcefulness required to make the best of things which the younger generations alive in the 2000s have lost to an extent. Also consider that some of the older characters may well have grown up during the war years or before, or at least in the midst of postwar austerity (rationing in the UK lasted well into the '50s) and are used to making the best of adverse conditions.