Ten years on from the referendum, Brexit still shapes British politics. It has smashed the two-party duopoly and continues to divide the country. Keir Starmer’s struggle to remain prime minister after last week’s drubbing for Labour in elections in England, Scotland and Wales is proof of that.

Voters took politicians at their word after the decision was made to leave the EU. The reason “Take back control” worked as a slogan was that it chimed with the public mood in large parts of Britain.

For years it had been clear that the UK’s economic model was only working for the better-off parts of the country. Globalisation might be bringing rich rewards to London and the south-east, but it isn’t to towns in the north hollowed out by deindustrialisation and austerity.

But taking back control also meant Britain could no longer use the EU as a reason for passivity. Politicians had become well versed in using Europe as an excuse for inactivity, but after Brexit this line of argument no longer washed.

The UK had to solve its own problems. It was no longer bound to adopt EU regulations. It could set its own trade policy. It could, if it chose, follow the example of east Asian economies and systematically rebuild manufacturing using tariffs, subsidies, government procurement and capital controls. But if the freedoms were not used, then nothing would change. And if nothing changed, politicians at Westminster would feel the full force of the public’s anger. There could be no hiding behind Brussels any more.

Ironically, the one sector that has benefited from Brexit freedoms has been financial services, in which both the previous chancellor, Jeremy Hunt, and current one, Rachel Reeves, have adopted a lighter-touch regulatory regime. Governments have had a clear strategy for this already powerful bit of the economy, and that strategy has worked. The City is thriving.

But that’s the exception. Voters young, middle-aged and old think their government should be doing more for them after a period of flatlining living standards stretching back almost two decades. In all parts of the UK, from London to the north of Scotland, they have reached the conclusion that neither Labour nor the Conservatives are up to the job. Neither party has convinced voters that they have a plan for getting Britain out of its mess.

Punishment has been swift and brutal. The Tories won a landslide victory in 2019 and then suffered a record defeat in 2024. Less than two years after winning a landslide of its own, Labour’s massive losses last week were the consequence of a government being squeezed by the Green party to the left and Reform UK to the right.

The Greens and Reform are like chalk and cheese, but one thing going for both parties is that they are untainted by failure. The Greens did well in the parts of the country that voted strongly for Remain in the referendum, while Reform UK cleaned up in Brexit-voting areas.

Those angling for Starmer’s job need to be aware that things are likely to get worse for Labour as the full impact of the wars in Iran and Lebanon are felt. Over the coming months, growth will slow and inflation will rise. Living standards will come under renewed pressure as the costs of energy and food rise.

Starmer’s latest reset earlier this week was an exercise in triangulation. He is seeking closer relations with the EU without rejoining the single market or the customs union, let alone pledging to hold another referendum. This strategy is doomed to failure, and not only because Starmer is to the public what kryptonite was to Superman.

Logically there are only two coherent approaches. One is to use the opportunities provided by Brexit to experiment with different ways of doing things. With its massive majority in 2024, Labour had the chance to do just that but never showed any real inclination to do so.

The other approach says Brexit was a mistake that should be reversed. If, as Starmer appears to think, the economy has suffered severe damage as a result of leaving the EU, then he should be campaigning to rejoin rather than fiddling around with exchange schemes allowing young EU citizens to come to Britain.

For those who supported Brexit in 2016, the arguments have not changed. Far from challenging the US and China, the EU is dying on its feet. Germany and France – the EU’s two biggest economies – are both in serious trouble. Stifled by neoliberal dogma and red tape, Europe shows no sign of regaining its economic dynamism.

The worldview of those who opposed Brexit has not changed either. The EU remains the UK’s biggest trading partner, so it makes sense to make trade as frictionless as possible. Donald Trump’s isolationism simply adds weight to the argument for closer cooperation with the EU.

Starmer is trying to ride both of these horses at once. His middle way is an attempt to win back Labour defectors to the Greens while telling those who have abandoned the party for Reform that there will be no Brexit sellout. What he is proposing is the worst of all worlds: accepting limits on Britain’s room to manoeuvre for no demonstrable benefit.

This approach will please neither remainers nor leavers. Nor will it disguise the fact that Starmer’s government is responsible for its own mistakes. Of which there have been far too many.

• Larry Elliott is a Guardian columnist