Leader: Anti-big-bootism: a timely lesson for Mr Blair

"You must never forget that what the public giveth, the public can take away." How very true. Like so many of the Prime Minister's utterances, his interview with The Sun two days before the by-election trod the fine line between homespun banality and disarming self-criticism. On 1 May, all over the country, they gave. On Thursday, in Uxbridge, they took away.

Tony Blair also said: "I'm pleased with the start we've made but we've got to keep our eyes on it the whole time, not get arrogant, not get too big for our boots." This was almost exactly the message about to hit him between the eyes from the voters of the outer London suburb.

Despite yesterday's attempts to put a brave face on Labour's defeat - "always a tall order", "no Referendum Party candidate" - it was an important check to the ambitions of the new government. Of course, the by-election makes no practical difference, but it has punctured the air of electoral inviolability that surrounds Mr Blair. It was bound to happen eventually, but for it to happen so soon, after such a euphoric post-election plateau, is a vital corrective to some of the more extreme talk of New Labour's absolute hegemony.

Uxbridge matters, too, because there will be a lot more of the unpredictable messiness of democracy, once Labour's reforms start to work through. The referendums in Scotland and Wales should produce the answers Mr Blair first thought of, but beyond them there are European elections under a new, fairer system; a wide-open referendum on the voting system for the House of Commons; and elections in Scotland, Wales and London. The mayoral "primaries" in the capital, to choose the candidates for each of the main parties, should be particularly entertaining.

Privately, Labour were hopeful of winning Uxbridge: it would have been the first time the governing party had gained a seat at a by-election since Mitcham and Morden in 1982, when the opposition vote was split between Labour and the sitting MP who had defected to the SDP. It would have provided the fairy-tale ending to the story of the first 100 days - young prince woos reluctant voter, is given the chance to prove himself, dazzles her, and finally wins her heart and leads the Natural Party of Government happily ever after. Which is why the by-election was fought hard, with the same total professionalism as Labour's general election campaign.

It is also a large part of the explanation of why Labour was rejected on Thursday. The voters of Uxbridge withheld their endorsement of Mr Blair because they did not want to countersign a blank cheque. It was less that they disagreed with anything the Government has done, more that they do not want it to get too big for its boots - as Mr Blair said (and he was probably quoting the focus group transcripts). Anti-big-bootism is perhaps the most powerful force in British politics, and long may it remain so. It is a fitting memorial to Vincent Hanna, who died last week, that the by-election now has an established role in the British constitution as an institutional form of unruly heckling.

Mr Blair needs to take less notice of the specific reasons which have been put forward to explain Andy Slaughter's failure to capture the Tories' 724 majority, although each does contain a lesson.

The most compelling is the local factor. John Randall, the new Tory MP, is definitively local: the managing director of Randalls, the department store founded in the town by his great-grandfather in 1891. Mr Slaughter, by contrast, was airlifted in from Hammersmith, and there is nothing so anti-metropolitan as the feeling of an outer part of London towards an inner. Labour dissidents have made too much of the decision to drop the "old Labour" candidate who fought the general election, David Williams, and replace him with a Blairite. The voters of Uxbridge were not criticising the Mandelsonian centralisation of the party, they were simply expressing a deep, localist prejudice. As William Hague ponders the need to imitate Labour's professionalism, he should take care. Modernise, by all means, but respect local roots.

The other possible causes of Labour's defeat include the fact that the middle classes feel clobbered by a tax on their pension funds and by parents being forced to pay more for their children's higher education. Neither factor can have swayed many votes in Uxbridge, although it is surprising that the Dearing proposals should have been so badly handled - under them, parents will pay no more than now.

The most important lesson from Uxbridge, however, is that the Government must not become, or be seen as, arrogant. It was unfortunate, therefore, that on the day of the by-election, a spokesman for the Prime Minister should have raised the possibility of using taxpayers' money to fund a libel action on behalf of Lord Simon against the Leader of the Opposition. That would have a chilling effect on free speech, and we do not believe it will happen. It was a foolish threat to issue.

Mr Blair, as ever, uses the right words. "For me the important thing is to keep in touch with the people all the time," he said on Tuesday. On Thursday, the people of Uxbridge got in touch with him, administering a gentle slap across the face. It was a little sharper than prime-ministerial walkabouts or deferential question-and-answer sessions. But it will do him and his government a power of good.