"Oh mate, the missus and the ex! Welcome to every man's worst nightmare."The return of Sarah Jane Smith and K9 Mark III, who (on screen) last appeared in "The Five Doctors" in 1983. This episode pretty much singlehandedly spawned The Sarah Jane Adventures, giving another generation of children the gift of Elisabeth Sladen. It also holds significance as the first episode of the modern era of Doctor Who to confirm that the new series was set in the same continuity as the 1963-89 original series (prior to its broadcast, fandom was split on this issue).
— Mickey Smith
So there's a certain Perfectly Ordinary Comprehensive whose Perfectly Ordinary Students are absolutely whomping the competition in the school ratings, with enough time left over in the school day to calculate pi to infinity, invent time travel, etc. They're led by new headmaster Anthony Stewart Head, whose hobbies include looking Obviously Evil, cackling maniacally, Chewing the Scenery and chewing on the kids.Sensing high weirdness afoot, the Doctor has gone undercover as a Perfectly Ordinary Substitute Science Teacher, dragging Rose along to serve as a Perfectly Ordinary Dinner Lady. Rose is a bit miffed that she pulled kitchen duty, but consoles herself with the happy thought of all the chips she can eat. In fact — childhood obesity epidemic be damned — at this P.O.C., school lunches are not only free, but also mandatory.Somebody else's weirdness detector has pinged, too: Intrepid Reporter Sarah Jane Smith (Elisabeth Sladen), companion to the Third and Fourth Doctors, has turned up at the P.O.C. to see what's afoot. It's been thirty or so years since she left the Doctor, in her timeline, and several hundred years in his. He recognises her but doesn't give himself away, only to come clean when Sarah Jane sneaks into the school at night and finds where he's parked the TARDIS. Here the picture goes all swimmy and blurry for some reason.By the time it clears up again, the Doctor has provisionally identified the cafeteria's chips as the source of the kids' mysterious intelligence. K9 (pulled out of Sarah Jane's car boot, and fixed by the Doctor) identifies the frying oil as "Krillitane Oil", which identifies the baddies as Krillitanes, a bunch of nefarious shapeshifters.So, OK, villain identified — but what's up with making the kids smarter? Why, so they can solve the Skasis Paradigm, of course! The Skasis Paradigm is a grand unified theory of everything that can rebuild the universe and space and time. The Doctor is eye-rollingly annoyed at yet another group of beings who want to take over the universe and remake it in their image... but then the head Krillitane surprises the Doctor by offering him the top job.Also, Sarah Jane tells the Doctor that she spent the last few decades waiting for him, unable to fall in love again, unable to forget him, unable to trust and unable to live happily as a normal human. The Doctor mumbles something almost resembling an excuse as Rose looks on in horror at what apparently awaits her. Noticing what the Doctor now means to Rose, Sarah Jane gives Rose some pointers on having "a relationship" with the Doctor, and the two bond after some initial awkwardness. Meanwhile, Mickey gets acquainted with K9 and realizes that he's not much more than The Team's "tin dog".With the Villain of the Week appropriately vanquished by K9, having blown up the Krillitane oil and a portion of the school as well as himself, the Doctor prepares to once again make his departure without so much as a proper goodbye. Sarah Jane isn't having any, and finally gets the goodbye for which she's been waiting three decades.
Sarah Jane: No, say it. This time, please, say it.Here he picks her up off her feet in a hug for the ages, and for a moment, we catch a glimpse of a much younger Sarah Jane Smith....No, whacking the screen is not going to make it less blurry.He vanishes again, but leaves his beloved Sarah with two things: badly-needed closure, and a new K9 model. However, this isn't the last we've seen of Sarah Jane, and she'll return in series 4.
The Doctor: Goodbye — my Sarah Jane.