Rachel Cooke thinks she’s seen this coming-of-age drama before.

I wanted to love White Heat, Paula Milne's much-trailed new drama series (Thursdays, 9pm). I hoped it would be as good and as moving as Our Friends in the North, whose scope and pathos it clearly has in sight. But on the evidence of one episode, this one looks like being a ropy ride. It's not the cast, which is great. Nor is it the look of the thing, so authentically smoky and brown (there are so many man-made fibres on display, you can practically hear the static). No, it's the writing that fatally lists and creaks. Undoubtedly someone, somewhere, in about 1958, did once tell his ambitious teenage daughter that higher education "is not for the likes of us". But when I hear this line in scripted dialogue, it makes me want to keen and tear at my clothes.

In essence, White Heat is a flashback. The main storyline begins in 1965. Churchill lies dying - sound the scriptwriters' klaxon for pointed historical timing! - and in a grotty part of London, a poor little wannabe-communist rich boy called Jack (Sam Claflin) is auditioning flatmates. Meanwhile, in 2012, in the same corner of London, Charlotte (Juliet Stevenson) arrives at the house she once shared with Jack and several other students. Its owner has died (we don't yet know if this was Jack), and she and her remaining former housemates, who have mysteriously inherited it, must pack up its contents before it is sold.

As set-ups go, this is painfully contrived. Ditto the group of students whom Milne has brought together, Open University-style, to illustrate changing social attitudes. Jay (Reece Ritchie) is Asian and gay; Orla (Jessica Gunning) is Northern-Irish Catholic; Victor (David Gyasi) is black; Charlotte (Clare Foy) is a home-counties feminist with a newly minted prescription for the pill; Lilly (MyAnna Buring) is arty northern, with parents who don't understand her; and Alan (Lee Ingleby) is a working-class Geordie who is determined to better himself. Ye Gods. If Jack doesn't turn out to be a transvestite, I am going to feel really let down.

In 1965, the characters have heated debates - Churchill: hero or hypocrite? - and attempt self-fulfilment. Charlotte reads a few pages
of Lady Chatterley's Lover and timidly masturbates. Lilly, whose figurative nudes her lecherous art tutor regards with some scorn, smears her naked body with red paint, and rolls across a large piece of paper. Alan, a Conservative counterpoint to everyone else's second-hand
radicalism, trots off to the dead prime minister's state funeral with Jack's father, a rich and smug MP. (The establishment, eh? When will it ever change?)

And in 2012? Well, the characters who've arrived so far mostly just stand around looking pained and nostalgic. One gathers that something bad happened between them a long time ago (most likely it has to do with sex; they're baby boomers, after all). This end of the plot is vaguely intriguing, being vastly less predictable than the mini-skirts-and-white-plastic-boots end. But it's disconcerting that the older Charlotte is played by Juliet Stevenson who, at 55, is surely ten years too young for the part. Still, at least she's in the right ballpark. The older Jay - when he finally turns up - will be played by Ramon Tikaram who, at 44, was not even born in 1965.

Will I tune in next time? Probably, albeit with less enthusiasm. The truth is that the older I get, the more I hanker for drama that tells the story of my family (working-class grandparents, grammar school-educated parents, er . . . me) - and so few writers, these days, seem interested in that particular sweep.

We have historical series, and we have contemporary stuff but the decades in between - years that still play an important part in our collective psyche - are relatively rarely examined and almost never deeply. In this sense, Milne is kicking her ball at an open goal. All we can hope is that down the line she will resist the temptation to turn Alan into an ideological Thatcherite and Charlotte into a long-term resident of the Greenham Common peace camp. Can she do it? It'll be tricky. For the tick-box TV dramatist, the lure of loud pinstripes and a certain kind of dangly earring are powerfully strong.