Last Night's TV: Lennon Naked, BBC4<br />Peckham Finishing School for Girls, BBC3

Lennon Naked began with a splash – a late-period John in what appeared to be mint condition plunging into the pool of his stockbroker belt mansion to the sound of "Come Together". The device might have felt a little overfamiliar (how many times has the off-the-peg transcendence of an underwater shot been employed in such things?), but it was all but impossible to resist the jolt of that music – a cameo appearance by the real thing in a drama that was largely going to be a triumph of similitude. Even more reassuringly, Robert Jones's script instantly showed that it had got the weight of Lennon's wordplay. A jump cut deprived us of the final resolving cadence of the song and plunged us again, back to Beatlemania, as John and Brian Epstein made a scrambled getaway down a fire escape and John demonstrated the rasp of his wit. "Kiss 'im," he says as fans beg for contact. "'E's never been kissed by womankind... or unkind." And the joke scrapes close to unkindness itself, a teasing poke with just enough thrust in it to hurt, but not enough to make the malice deniable should things turn nasty.

Jones's biopic has been scheduled as a contribution to the BBC's Fatherhood season and you could take it as male companion piece to Sam Taylor-Wood's recent film, Nowhere Boy, which traced the origins of Lennon's discontent and disruptive talent down the matrilineal line, through his relationship with his Aunt Mimi and his erratic mother, Julia. Both films feature Lennon's Merseyside version of Sophie's Choice – taken to Blackpool by his warring parents and forced to choose between them by the father. The five-year-old John first took his father's hand but then turned to his weeping mother, only to see his father walk out of frame for 20 years. Jones's drama began with the first awkward reunion with Freddie Lennon, as they met up in a London hotel room, where Freddie's inadequate clichés were given a brisk roughing up by Lennon: "You look after yourself, John," his father says as they part. "I do... that's right," replies Lennon bitterly.

The bitterness was the top note in Christopher Eccleston's performance – vocally pretty sharp to my ear, though I wasn't listening with a worshipper's vigilance. This was a Lennon exasperated to find himself one of "the nation's little pets" and venting his unresolved anger against anyone available. On the rare occasions when his father is on hand he's the recipient: "Who do you think this disreputable get is Julian?" is the question that introduces Lennon's son to his grandfather, when the latter arrives to stay in his Surrey country house. But Cynthia, Lennon's first wife, gets worse, verbally needled by John until he finally delivers the legal coup de grâce: "'I must have loved you once, but I don't anymore.' Will you communicate that to her?" Lennon tells his divorce lawyer, unremarkable as marital bile but for the fact that Cynthia is sitting three feet away from him when he says it. And his friend Pete – one of the few people prepared to tell him how badly he's behaving – is rewarded for his honesty with a cruel sneer ("You're a shopkeeper, Pete... keep your little thoughts to yourself"). It wasn't a flattering portrait, to put it mildly, though it came with the fierce mitigation of Lennon's insecurity, which can't be eased by the generalised adoration of stardom: "Everybody loves me?" he says at one point. "That's like saying nobody does." In the end, though, impressively performed and tightly written as it was, it wasn't clear that it took you any deeper into Lennon's pain than his own songs have been doing for years. Lennon Naked, perhaps, but still not much more than skin deep.

"So you've come to Peckham to see the poor people," said a local to one of the moneyed participants in Peckham Finishing School for Girls. The short answer to which was "yes", the dubious conceit behind the programme being to match up four privileged young gals with four inner-city counterparts who missed out on a silver spoon at birth. It's essentially My Fair Lady in reverse – the four blonde show ponies who have taken up residence in a Peckham council flat will be taught important lessons in deportment and behaviour by a spell in the inner city. The Henry Higgins of the operation is Peaches Cadogan, a formidable youth worker, whose job it is to smooth ruffled feathers whenever the blithe flippancies of the posh girls scrape against the raw sensitivities of the street girls.

To be fair to it, it is about the erosion of prejudices, although in this regard the Peckham girls are the biggest beneficiaries. We learned in last night's episode that posh girls can be bullied too, but that revelation paled into insignificance against the history of serial abuse, violence and neglect that the Peckham crew have endured. What the outsiders take as feral aggression is actually scar-tissue, a thickness of skin acquired from repeated wounding. The posh girls might charitably be described as slow learners. "It's just not like going to Champney, is it?" one said to a friend after a day's work experience in a Peckham beauty parlour. Another excruciatingly tried out her street talk on the regulars in a Peckham pub, blithely unaware of how condescending and touristic this would sound. But... very slowly... they are getting there. Thanks to Peaches, there even looks to be a good chance that they'll get home without the word "finishing" taking on a terminal aspect.