John Rentoul: Power dressing, Cameron-style We're all cross-dressers now Dave Through the Looking Glass

Straw has taken a right-wing position on an issue that is proxy for race

Would it be unduly cynical to attribute to Jack Straw an ulterior motive for lifting the veil on non-Muslim unease about women with covered faces? Not at all, according to the BBC, which uses the licence fee to tell us - as factual news on Radio 4 - that it was an attempt to further his ambitions to be deputy Labour leader. Straw was so impressed by the way John Reid, the current Home Secretary, raised his profile by asking Muslim parents to keep an eye on their children, the BBC implied, that the former home secretary thought he might get in on the Islamophobic action too.

Even as commentary it is daft; as news reporting it is inexcusable. The idea that the Labour MPs and Labour Party members who elect the leader and deputy leader would rally gratefully to the standard of a candidate who takes such risks with liberal squeamishness is bizarre. While the idea that Reid's popularity rose because he said right-wing things about Muslims is simply a misunderstanding. The Home Secretary impressed people with his decisive handling of the airline terrorist scare, and because he was seen on television to be standing up to an extremist ranter.

It is possible to be cynical about Straw's motives. No doubt he would like to be deputy leader - and deputy prime minister. But it is a crowded field, and the rules require candidates to be nominated by 45 MPs, which means in practice that only three or four will stand. Currently, the candidates are likely to be Hilary Benn, Alan Johnson, Harriet Harman and possibly Jon Cruddas. It is not immediately obvious that the best way to squeeze an extra name onto the ballot paper is to adopt a position widely regarded in the Labour Party as right wing on a cultural issue that is proxy for race.

The more conspiracy minded at Westminster have suggested that Straw was trying, on behalf of his patron Gordon Brown, to steal a little of Reid's thunder, in order to pre-empt the threat to the Chancellor for the top job. That is too clever by half, if not three-quarters. The same rule that makes it unlikely that Straw will be a candidate for the deputy leadership makes it difficult for Reid to run for the leadership. The Home Secretary is highly regarded by the public. One poll suggested that he would, by a small and provisional margin, do better against David Cameron at the next election. But his populist lines on crime, terrorism, immigration and foreign policy are hardly designed to maximise support among fellow MPs. Roy Hattersley may not be an MP any more, but there are plenty like him who say they would shoot themselves if Reid became leader. Alan Johnson, the Secretary of State for Education, is a plausible candidate against Brown because he, unlike Reid, can appeal to left-wing MPs as well as to Blairites. (Although he is rather less plausible after a desperately dull conference speech.)

The fact that Reid is still unready to run (he would need months of decisive polls in his favour to show Labour MPs in marginal seats that he is their key to re-election) does not mean, of course, that Brown is not out to get him. But Straw's article is not an assassin's bullet.

No, I think Straw said it because it is what he thinks. Sometimes politicians say something because they believe it to be in the national interest. If there were any calculation to it, it would have been that he saw a chance to seize the initiative from the Conservatives. If there is a conspiracy, it is one that unites a large part of the Labour leadership, and it is directed at David Cameron. Cameron has been forced to retreat from the areas of immigration, race and culture for fear of renewing a right-wing Tory stereotype, and many ministers are determined to move into that territory and claim it for Labour.

Indeed, last week was like a lost chapter of Through the Looking Glass. How we liberals laughed when Cameron, at his most Blairishly sly, got the Tory conference to clap "Marriage is a great institution and we should back it", and then to clap again when he added, in effect, "including gay marriage".

But how we hesitated when he extolled the NHS as "a symbol of collective will, of social solidarity". Tories as social liberals we have become used to, since the Great Portillo U-turn. But Tories as collectivist defenders of the works of the Sainted Attlee? That requires an adjustment. It shouldn't really, of course. The idea that the Tories opposed the founding of the NHS is one of the longest-running libels in British politics. Yes, they voted against the NHS Bill in 1946, but their objections were to the structure, not the principle. The Conservative manifesto of 1945, like Labour's, promised to set up a national health service free at the point of use. And, since Margaret Thatcher accepted Kenneth Clarke's decision in 1988 to preserve the essentials of a tax-funded free system, there has never been a serious possibility that the Tories would do anything else. It is about time, therefore, that the party gained some advantage from that accommodation to political reality.

Cue another burst of the fashionable and pseudo-sophisticated observation that Labour has moved to the right of the Tories or that Cameron has moved to the left of the Government. Not so. That is an optical illusion caused by the fact that the electoral centre ground on issues such as crime and immigration is further to the right than sophisticated opinion would like. Or by the folk myth that the Tories want to destroy the NHS.

The thinking behind Cameron's approach was laid out with some intellectual clarity by his adviser Danny Kruger in last month's Prospect. It is to reclaim community, society and the soft virtues for the Tories. Of the great ideological trinity, he said, liberty is the Tory value, equality belongs to Labour and fraternity is in contention. Hence Cameron's laying claim to the idea of social solidarity. "The battleground has shifted," wrote Kruger, "but the same armies are fighting, and ultimately for the same causes."

So it would be a mistake to see Straw's attack on the veil as a mere ploy. But it would be more of a mistake to think that the convergence on the centre ground has gone so far, and even that the two parties have overshot each other, that there is little to choose between them.