IN the end, it was Labour's day if it was anyone's.

In parts of England, the sentiment among Labour activists was euphoria, while in Scotland, it was largely relief, at the expense of misery for the Liberal Democrats and, in Glasgow, disappointment for the SNP, though the party performed strongly overall.

For Labour, its successes in Scotland will be particularly sweet. The loss of certain key seats in last year's Holyrood elections led to the redrawing of Scotland's political map, a change that looked like feeding through to the next General Election, to Labour's considerable detriment; this result makes that seem less likely.

Johann Lamont must now be hoping that this signals a lasting change in Labour's fortunes. She claims: "The tide is going out on Alex Salmond".

In truth, it would be unwise for anyone to draw conclusions about the likely outcome of the next Holyrood election, or the independence referendum, from these results. True, there was a higher-than-feared turnout in many areas, better than the estimated UK-wide average of just over 30% (Glasgow excepted). Voter motivations when casting their council votes, however, are mixed and unclear (one person may vote over the state of the roads while another against the Prime Minister), making them a notoriously unreliable predictor of future voting trends.

That means there is all to play for in the next Holyrood elections, and in the referendum, though Labour could justifiably feel a little more confident today about both, while the SNP will be taking stock of the need to redouble its efforts to achieve its goal of independence.

The totemic Glasgow result in particular will disappoint the SNP – it has failed to seize control in spite of a huge effort and the fact of Labour having suffered public ructions post-Purcell, and last year when 20 councillors were deselected; being in power for 33 years apparently isn't such an affront to voters after all. The SNP also failed to become the largest party in Edinburgh.

The party has nevertheless performed strongly, particularly given that it has been in government now for five years, taking control of both Dundee and Angus councils and achieving the largest share of seats, but it has not reproduced the stunning successes of last year against Labour and the fear in Nationalist ranks must be that its popularity with Scottish voters may have peaked. It is hard to know whether it has suffered because of Alex Salmond's links with Rupert Murdoch, but the possibility will concern party managers.

The biggest losers were undoubtedly the Liberal Democrats and the Conservatives. For the LibDems in Scotland, there was a nightmarish sense of deja vu, with the party losing more than 70 seats, one year on from its disastrous performance in the Holyrood elections.

In Edinburgh, the LibDems were reduced to three from being the largest party, with former council leader Jenny Dawe among the casualties. UK-wide, the party appears to have achieved its smallest number of seats ever, which, combined with its low popularity in the polls and poor showing in last year's Holyrood elections, has undermined decades worth of improving fortunes. Those fortunes are unlikely to recover until they break what many see as a Faustian pact with the Conservatives, though it is doubtful that the party can afford to leave government, given the likelihood of annhiliation at the polls in the General Election that would follow.

The Conservatives have little to celebrate either, losing more than 15 seats in Scotland. It was part of a day of heavy losses UK-wide, not helped by what has been described as the post-Budget omni-shambles, a dark narrative that shows little sign of ending satisfactorily for David Cameron. The rejection of elected mayors in eight out of 11 cities which held referendums on the issue – a policy personally championed by David Cameron – was an added blow. Boris Johnson's likely success in London will only be a small consolation.

There was good news, though, for the Green Party, which has had one of its best elections to date, largely at the expense of the Liberal Democrats, going from eight councillors to 14.

It is the Labour revival, however, that these elections will be remembered for, both north and south of the Border, not that Ed Miliband or other senior Labour figures have made the mistake of sounding triumphalist about it. Even Neil Kinnock fared better in local council elections than this, but he didn't make it to Number

10. Mr Miliband is not yet Prime Minister-in-waiting.

Nevertheless, it does make him a much better prospect as the man to take Labour into the next General Election, not least because of the party's important council gains in the south of England from Tories and Tory/LibDem coalitions and taking seats in the Prime Minister's own true-blue back yard of Witney.

The more immediate question, however, is where the results leave the Tory/Lib Dem Coalition. It was already clear by yesterday lunchtime that many in each party were turning on the other, with the main charge coming from Conservative ranks, blaming the LibDems for championing "barmy" policies such as Lords reform and gay marriage.

The real root of the Coalition's woes, however, is much more straightforward: it's the economy, stupid. In truth, implementing an austerity package on the scale that any of the three main parties were advocating in the run-up to the 2010 elections would have resulted in a bloody nose two years down the line, whoever was in power. If the Westminster Government has been on trial in this election, it is over the depth and speed of the austerity cuts. The decrying of Lords reform, green taxes and gay marriage by disgruntled Tories, misses the point and the pressure by some activists for a lurch to the right, would certainly be disastrous for the party, as its history since 1997 shows.

Time for a reality check, anyone?