This week a number of Conservative MPs, ministers and canvassers told me that it would be a good night for the Tories in the local elections if they managed to hold on to one of Wandsworth, Westminster or Kensington. So, on these grounds, it ought to be a sensational and unprecedented turn of events that the Conservatives have managed to keep hold of not one, not two, but all three of these councils. Adding the cherry on to this already multi-layered cake is the fact that the Tories have also managed to take control of Barnet council – high on Labour’s hit list until the most recent antisemitism row.

However, while there will be audible sighs of relief in CCHQ this morning, these results will not be enough to trigger champagne for breakfast. The party’s better-than-expected result is as much down to a masterful campaign in expectation management as big gains. While the Conservatives have managed to stave off disaster, make progress in some target seats and hold the line in difficult circumstances in parts of London, this is an election in which no party has done exceptionally better than the other. Labour’s problem is that it let expectations run so high, even relative success now looks disappointing.

Were these results to be projected in a general election, the Tories would lose seats. They would be at 305 seats – still the largest party by some way but well short of a majority.

But the result remains a significant boost to the Tory party – though not for the reason being spun. For both Theresa May and Jeremy Corbyn, the path to winning complete power looks unclear, with one party excelling in cities and the other outside them. Confusion and disagreement remains over how the Tories could win a majority at the next election. And these results aren’t bad enough for the Tories to desert London entirely in their general election strategy. A debate will need to be had over how much places such as Bolsover and Bishop Auckland should be prioritised over places such as Battersea.

The reason the result is important for the Tories is psychological. The better-than-expected result helps to burst the bubble on the Corbyn complex and shows that the momentum behind Labour is not as unstoppable a force as previously thought. After the disastrous snap election, the Tories were walking around parliament as though they had lost and Labour as though they had just won. Some Labour frontbenchers even claimed they had. Since that vote, Labour’s top command have been keen to pitch the idea that an election is imminent – that the party was so close the last time round that a second stab would ensure it. Meanwhile, the Tories are so terrified of another election that they wish to hold it off indefinitely.

Last night suggests that this is not the case. Despite mass campaign efforts in London, Labour has not made the gains many had hoped and the Tory vote has proved firmer than many had expected. No Tory MP – other than perhaps Johnny Mercer in Plymouth – will have more reason to be worried about their seat than they had on Wednesday. This is not to say that the Tories are out of the woods. If last year’s election should have taught us anything it’s that a local election offers no guarantees about the general.

But for morale purposes, today’s results are just the tonic for a tired Tory party. Corbyn’s messiah status has taken a knock. The memories of the Labour leader leading the charge at Glastonbury that spooked the Conservative party so much now seem a more distant memory. The local elections have offered wounded Conservative MPs a much needed reminder that elections can be won on bins rather than the Pyramid Stage.

• Katy Balls is the Spectator’s political correspondent