Aside from the deliberate snub to his deputy leader, Sir Keir Starmer’s reshuffle this week has widely been seen as a good one. Which, admittedly, is a bit like asking, “Apart from that, Mrs Lincoln, how did you enjoy the play?”

Yvette Cooper is expected to make life harder for Priti Patel, the Home Secretary. The quiet, methodical and serious Pat McFadden, new shadow chief secretary to the Treasury, has long deserved a seat at the table. Wes Streeting takes the high-profile health portfolio, a merited promotion, while Starmer has sensibly moved Louise Haigh away from the Northern Ireland brief after her calamitous suggestion that Labour would remain neutral in any future border poll. Her replacement, Peter Kyle, is one of the party’s most effective communicators.

All things being equal, this new team ought not only to give Labour in Parliament a fresh lease of life, but should remind the Government that there is actually a serious alternative to the Conservatives, and that they can’t necessarily take the next general election for granted. Improved performance on both sides of the House would be no bad thing for the country.

But there remains a fundamental weakness in Labour’s offer, one that has been exacerbated, not diminished, by this reshuffle. If Labour is to win the next election then its central mission has to be to restore trust in the party among Red Wall voters, people who supported Brexit and who, when faced with the choice between a party committed to overturning the referendum result and Boris Johnson’s promise to “Get Brexit done”, unambiguously chose the latter.

Starmer himself has struggled to escape his own legacy as shadow Brexit secretary under Jeremy Corbyn, when he contrived to frustrate Britain’s departure from the EU. It was he who — in an act of rebellion against his leader — promised his party’s conference in 2018 that any second referendum would not just be held to confirm the terms of our departure but would include a Remain option on the ballot paper.

While the shadow cabinet has now been strengthened with experience and political ability, Starmer is taking a big gamble in placing his hopes on a group of individuals who fought at his side to frustrate the will of the Leave-voting majority.

The new shadow foreign secretary, David Lammy, for instance, has fiercely decried calls to “appease” Labour voters who supported Brexit, insisting they had fallen for the lies of the Leave campaign, and once said that describing Tory MPs in the European Research Group as “Nazis” was “not strong enough”.

Cooper herself has already paid a heavy price for her Remainer tendencies, seeing the majority in her Northern seat slashed from nearly 15,000 to barely 1,000 at the 2019 election.

Both Streeting and Kyle are known as doughty campaigners for Britain’s EU membership. The latter was one of the chief architects of a parliamentary plot to force a second referendum offering a choice between Theresa May’s Brexit deal and to Remain.

While Starmer appears to care little about the Left-Right balance of his frontbench, the pro-Remain balance is likely to leave his party dangerously vulnerable in the very areas where it needs to prosper at the next election.

The issue for the Labour leader is that this is a problem he can hardly avoid. Since the late 1980s there has been no mainstream tradition in Labour that favoured leaving the EU. That led, by the time of the referendum, to a complacent, virtually unchallenged assumption that the party was, and always would be, pro-Brussels. Those who gained prominence in Parliament in the last 30 years, therefore, have been overwhelmingly of the same school of thought. Starmer, in other words, has little choice but to pack his shadow cabinet with Remainers.

That presents a huge risk for him as the next election approaches. Voters in Red Wall seats still feel angry about Labour’s patronising dismissal of their decision to vote Leave. Even if they’re ready to forgive, it will be difficult for them to forget while such prominent Remainers — who themselves have never recanted their previous positions — are seated around the shadow cabinet table.