Who’s on what side in Labour’s policy on immigration? It depends on your perspective.

Yesterday, I detailed why and how the leadership has re-oriented its stance on immigration. Today, in the Guardian, Keir Starmer, the shadow secretary of state, is said to be “furious” about the new direction of Labour policy on Brexit.

Jeremy Corbyn himself remains fiercely pro-immigration, and crucially, Diane Abbott, the shadow home secretary, who exerts a significant influence on Corbyn on policy and political matters, continues to remain a strong advocate for a robust defence of migration.

But the interventions of John McDonnell, who has signalled that Labour will no longer oppose Brexit, and Clive Lewis, who sounded a more sceptical note on migration, have brought the divide into the open.

Lewis’ allies insist, however, that his role has been overplayed. On Twitter, Lewis has characterised his stance as “don’t pull up the drawbridge, protect workers”, while friends have confirmed that when he appeared to suggest that the benefits of immigration were up for debate on Sky, he was highlighting that the macroeconomic benefits have not been fairly distributed, not that they are illusory. As for his interventions, they were “off-the-cuff”, rather than having been cleared with the leader’s office in advance.

Lewis sees the party’s woes over immigration as posing an “existential threat”, according to those familiar with his thinking. However, he agrees that the first policy priority has to be securing “tariff-free access” to the single market, but not membership. The divide between that and the Starmer position is that the party shouldn’t give up on single market membership while seeking some form of “adjustment” on free movement.

From a policy perspective, the gaps here are small; Starmer is keen to shoot for full membership but that is impossible to reconcile without accepting the four freedoms, Lewis is keen for tariff-free access which is likely where Starmer’s objectives would end up. In practice, the policy direction is the same: which ends up with Britain out of the single market, and therefore with an end to free movement.

(As a side note, it’s worth noting that, rightly or wrongly, both sides of Labour have largely given up the argument that immigration has been anything other than a negative on wages, particularly towards the bottom of the wage distribution.)

So why the divide? There’s another fight that – consciously in some cases and subconsciously on others – is playing on people’s minds. The question never far from people’s minds around the Corbyn project is who Labour’s next leader should be. John McDonnell, long regarded as the natural successor, is now seen to have missed his moment and in any case, is seen as unacceptable by some in the trade union movement.

On European issues, the bulk of Labour MPs, whether left and right are in the awkward position of triangulating around the membership’s position, which is to be both pro-EU – or at least, the softest of Brexits – and pro-immigration. Most Labour MPs are either opposed to one or both, whether that’s because of the restrictions imposed by single market membership to a more radical economic agenda, or the fear among many that Ukip will do to them what the SNP did to their Scottish colleagues.

As I’ve written before, Lewis is well-placed to occupy what may be the sweet-spot in the next leadership race – aligning with those who agree with Corbyn on the economics but fear that on security issues he is dead on arrival with the electorate.

Starmer is marking himself out as the natural occupant of what may be the best terrain to challenge that from: publicly supportive of the project, while explicitly more pro-European than either Corbyn or his successors from the party’s left.

But both Starmer and Lewis are also running the same risk: that their political journeys leave them without a natural base of support in the parliamentary party. Lewis has gone “on a journey” in the words of one MP, which means that he risks having alienated natural allies on the left while still being distrusted on the right, while Starmer’s decision to serve under Corbyn leaves him with the opposite problem.

Despite both being widely tipped for the top job in the press, the future may well belong to someone else. In the trade union movement in particular, there is a sense that the conversation over the party’s failure to pick a woman leader will intensify, and that, as well as the fact she is held to have done well as shadow chief secretary to the Treasury, will mean that a bigger profile will be carved out for Rebecca Long-Bailey, regarded by many influential Corbynites as the long term best bet for the succession.