Jane Clark does not, apparently, object to John Hurt's portrayal of her late husband on BBC4's The Alan Clark Diaries (Thursdays, 10pm), even though the dramatisation shows him wearing white shirts and he only ever wore blue. I do, however. Hurt captures the Tory's self-delusion and torment but not his glamour and flair. Hurt's Clark does not look smart, randy or arrogant enough. Clark constantly thought he was pre-cancerous. Hurt looks post-cancerous. He is too much Malvolio after his debagging, and although we see Clark poop-pooping down lanes in his vintage cars, we need more of Toad before his debagging.

We cannot blame Hurt, who is an excellent actor, but we can question a script that turns most of the jokes on Clark, something he would have hated. Everyone gets the better of him, from his secretary to the prime minister, and even his devilry is interpreted as naivety. Clark was no Machiavelli, but he was no Pooter either. For some reason, however, Jon Jones, who directed and wrote these six half-hours, has chosen to edit and cast the diaries so that they make Clark a pathetic rather than a contemptible cad.

The series begins with him at the death-bed of his father (Lord Clark of Civilisation fame), with Alan embarrassingly telling him he loves him and getting out as quickly as he can. From this moment of Oedipal awkwardness, we are invited to consider Clark's difficulties with women. To which I respond: what difficulties? Clark kept on board a wife who adored him, had no problem with working for a female boss and had sex with surprising frequency with women he fancied. Yet Jones emphasises his unconsummated passions, notably for his ice-maiden secretary when he joins the Department of Employment as a very junior minister. In fact, we never see him in bed with anyone apart from his wife. The series's discretion is its most extraordinary aspect, the more so given that the script consultant was Andrew Davies, whose normal rule is "add more sex". Maybe if this had been a BBC1 series it would have been different.

For all these disappointments, The Alan Clark Diaries is, nevertheless, a delight. In the first place, it is a chance to savour the diaries again and they are indeed a masterpiece. Clark's character assessments (or assassinations) as voiced by Hurt do much more than the actors to bring Tom King, Ian Gow, Peter Morrison et al to life. Wisely Margaret Thatcher herself, like Muhammad, is never shown full on, being represented merely by the back of her head (could that be a wig?) and her handbag, but her perfumed presence is everywhere. In his observation of Gow's grief when Thatcher begins to find her courtly lover's attentions irritating, Clark gives us a reading of the political parlour we would get from no one else.

And although the programme somehow thinks it is better than Clark, and goes to pains to show that he was entirely deluded about his own political pashes, its downbeat tone at least shows off his humanity. It is true that the downfall of others invariably lifted his spirits - one man's misfortune was another's ministerial reshuffle upward - but the victims were only politicians after all. When it comes to striking miners, who want only to work, or a heron whose only crime is to have a taste for the fish in his moat, he is compassion itself. The darkest moment comes when Thatcher bullies him to drop his anti-fur-trade bill. If he resigned over it, he muses, he would be the first minister ever to quit on behalf of "creatures who do not have a vote"; yet he cannot face a return to life with the buffers on the back benches.

I could watch much more of these programmes, and many more people would do so, were they not being confined to BBC4. I was pleased to see so many posters around town advertising the series on this remote channel but disappointed by the impoverished appearance of the production, which keeps rooms underpopulated and represents foreign trips with moving arrows on a map, like the beginning of Dad's Army. The production could easily be remade as a West End play of the Jeffrey Bernard is Unwell type, with a minimal cast and minimal sets.

It is one of the scandals of the current BBC that BBC4, which receives a universally good press and maintains the best values of the corporation's history, has a budget much smaller than the distinctly dodgy BBC3. BBC3 is not liked by the critics - which may not matter - but nor does it enjoy good ratings - which does matter, as its purpose is to pre-empt multi-channelled youth defecting from the BBC brand for good.

My solution is for BBC 3 to take up some of the more populist nonsense from BBC2 and for BBC2 to fill the gap by importing much more product from BBC4. To ensure it gets the right stuff and the programmes the appropriate funding, BBC4's controller, Roly Keating, should take over from Jane Root at BBC2. She can take over at BBC3. But that's enough recruitment advice. As for casting and who should have played Clark - well, Bill Nighy crossed with John Hurt would have been ideal, wouldn't it?

Andrew Billen is a staff writer on the Times