John Rentoul: All change at Crewe: is it Brown's Waterloo?

Every year, local elections are billed as a crucial test for the Government. They usually aren't, but this year they are. The opinion polls give a remarkably wide range of guesses, and no one has cast real votes in real ballot boxes since the Sedgefield and Ealing Southall by-elections, which came just three weeks after Gordon Brown became Prime Minister.

Thursday will be one of those anchoring points where we get a fix on politics and take our bearings. Despite the uncertainties of the opinion polls, we know the broad outlines of the story already, of course: bad for Brown; good for David Cameron. But how bad and how good will finally be triangulated without caveats about sampling, fieldwork dates and random error – although new caveats will come into play about turnout, local factors and how to calculate the national equivalent share of the vote.

With the opinion polls pointing in different directions in London, the result there matters as much to the pollsters as it does to Ken or Boris. The big question for them is whether they are still over-estimating Labour support, which they have done persistently since 1992.

If the London polls are exaggerating Livingstone's vote, not even the second preferences of the rainbow coalition of Greens and Liberal Democrats will save him. Even if he does hang on as mayor, Brown will not gain much credit and the results elsewhere will be reported as Labour's worst since the Spanish Armada, or some other resonant date. That much has been written already, and will be written again, several times, before Thursday, and while we wait for the second critical tranche of results (including London) on Friday, and afterwards.

But there is another big, hidden story this week, and that is the eclipse of the Liberal Democrats.

With all eyes transfixed by Brown's slow-motion disaster over tax rises for the poor, the fate of the third point in our irregular-triangle-shaped party system has been overlooked. Nick Clegg's failure to seize his chance is important because, when governments suffer transient and temporary problems, their support defects, transiently and temporarily, to the Lib Dems. But when Margaret Thatcher, John Major, and now Brown, suffered terminal damage, their support defected straight to the main opposition party and the Lib Dems have been squeezed.

That is precisely what has happened over the past six months. What is most surprising is that the election of Clegg just before Christmas had no effect on Lib- Dem standing. So Labour's lost votes are going straight across to the Tories. That is what Tory canvassers say they are coming across on the doorsteps. They would, wouldn't they? But there is a note of surprise in their voice that I haven't heard before. They also say that the 10p tax-rate issue has "cut through" in a way that few such issues do in retail politics – even though they admit that many of the voters who feel as if they have been personally hit by it probably haven't been.

It just goes to show that in politics you have to look after the pennies. If Senator Everett Dirksen were alive today, he would say of the Government underwriting Northern Rock and the inter-bank market: "£50bn here, £50bn there, and pretty soon you're talking about real money." But it is dropping the 10p tax rate, which costs the low-paid, at most, £2.50 a week, that is doing the real damage.

And it is the Conservatives that are benefiting. Unlike the Great Blair Disillusionment before the 2005 election, when Labour supporters parked their votes with the Lib Dems, this time they have gone all the way. Then the issue was Iraq – an issue that Charles Kennedy made the Lib Dems' own. Now the issue is tax – the word that runs through the Tory stick of rock.

Cameron recently told his aides that he thought Clegg had missed his chance to move the market. "You only get a few chances to define yourself as a new leader," he said. "When you are elected; your first conference speech; and your first Prime Minister's Questions."

In none of those did Clegg shine. When he was elected, he made a speech saying that he wanted a Britain "where social mobility becomes a reality once again, where no one is condemned by the circumstances of their birth". Brown or Cameron could, and often do, say similar things. This was accompanied by a YouTube broadcast that looked as if it had been filmed in a public convenience.

In his first speech to a large party audience, at the spring conference in Liverpool last month, Clegg's attack on the Tories' vision was: "They're in favour of winning; they're against losing; and that's it." Only once at Prime Minister's Questions has he scored a hit: last month on citizenship for the Gurkhas, a good question which he then wasted by switching to Iraq. Instead, his early memorable moments as leader were a party split over policy on a European referendum and an interview with Piers Morgan about his sex life.

On Thursday, therefore, the Lib Dems face a stiff test, with their national opinion poll rating three points lower than it was when they last fought these council seats. In London, Brian Paddick will be squeezed out.

Much of the pre-match analysis has suggested that Labour may be able to present Thursday's results as being not too terrible, because it was so unpopular in the wake of the Iraq war four years ago. But it is five points lower in the national poll averages now, and the Conservatives are six points higher.

Thus the political model has reverted to two-party competition. British politics seems to toggle between two models. Either discontent with the government goes to the third party while the official Opposition languishes, or it goes straight across. For most of her time at No 10, Thatcher enjoyed a divided opposition. Then came three by-elections in 1989-90: Vale of Glamorgan, Mid-Staffordshire and Monmouth, that Labour won from the government.

When the Tories dumped Thatcher, the Lib Dems started singing "Walking in a Liberal Wonderland" at by-elections again. It was only in the later Major years that Labour under Blair started winning by-elections again.

That is why the by-election in Crewe and Nantwich, caused by the death of Gwyneth Dunwoody, is so important. It is the next triangulation point on the political journey ahead. What is at stake is not whether Labour can hold the seat – it is a write-off – but whether it will be the Tories or the Lib Dems that win it. At the last election, the Tory candidate was in second place, and now needs an eight-point swing to win, but the Lib Dem candidate won a respectable 19 per cent share of the vote.

Both Cameron and Clegg desperately want to win this one. Just as the Lib Dems slowed the New Labour advance at the Littleborough and Saddleworth by-election in 1995, allowing Paddy Ashdown to dream of a partnership with Blair in government, so the Lib Dems could check Cameron's advance and establish their credibility as a force to be reckoned with in a hung parliament.

If the Conservatives win, it would be the first seat they have taken from the Government since the 1970s and would allow Cameron to start having those dinners at the Travellers Club with permanent secretaries that mark the beginning of the unofficial transition.

Suddenly, the Liberal Democrats matter again. This week, their weakness will allow a Conservative breakthrough. At the Crewe by-election, their showing will decide whether that breakthrough becomes a rout.