Ed Miliband had reason to look pleased. The election results were every bit as good for Labour as he could have hoped. In the spinning that preceded the count, the Conservatives set the Opposition a target of winning at least 700 council seats from the other parties to look credible, in the clear belief they would not reach it. Labour sailed past that figure yesterday.

In Scotland, Labour thwarted Scottish Nationalists' high hopes of seizing Glasgow city council. In Wales, Labour scored its best result since local government reorganisation in 1996. Even the London mayoral race – the one Labour had privately given up for lost – turned out to be much closer than most of the polling had anticipated.

The Conservatives can justifiably attribute their losses to the kind of unpopularity that afflicts governments after a couple of years in office – the so called mid-term blues. But losing about 400 councillors in a single day is a body blow to any party. That is 400 fewer committed activists putting life into the party at local level.

The picture for the Liberal Democrats overall is, if anything, even bleaker, since they lost about two of every five council seats they were defending, though they were able to take some comfort in gains made in places where they have a sitting MP. This included even Eastleigh, whose MP, Chris Huhne, has had a dismal year personally, but where his party now has 40, out of 44, council seats. For the Liberal Democrats, the results will inevitably prompt question about whether they should put more distance between themselves and their coalition partner.

Within the Conservative Party, the results are bringing to the surface long-rumbling discontent with David Cameron's leadership. The Prime Minister will inevitably feel his party tugging him to the right – trying, for example, to persuade him to abandon gay marriage and reform of the House of Lords. These issues are not on most people's political radar, but they are symbolic issues which aggravate the Tory faithful and go part of the way to explain the continuing rise of the UK Independence Party. Abandoning them might buy Mr Cameron some peace within his party, but would not win over anyone thinking of voting Labour.

Overall, if the voters had divided as they did yesterday in a general election, Labour would be back in power with a commanding majority, and Ed Miliband would be marching triumphantly into 10 Downing Street. But there is the rub. It was not a general election, and voters knew they could give the Coalition a bloody nose without having to ask themselves whether they wanted Ed Miliband and Ed Balls running the country in place of David Cameron and George Osborne.

Opinion polls show that, although the Labour Party is gaining from the Government's troubles, trust in Ed Miliband is not increasing, or not to anything like the same extent. And even if it were, there is no point in Labour or anyone else clamouring for an immediate election, because the Coalition has brought in fixed-term parliaments, meaning that it is another three years before the voters have to choose a new government. Nor, with their current levels of support, will either coalition partner want to force an election sooner.

The scale of Labour's local election victories has bought Ed Miliband time; talk of replacing him with someone who has more popular appeal will be silenced for the foreseeable future. While secure in his position as Leader of the Opposition, however, he is not established as a prime minister-in-waiting. Because of that, the week's successes may yet turn out to be Labour's false dawn.

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Cities reject Cameron's dream of mayors for all
Salmond setback as Scots nationalists fail in Glasgow