Should the Labour Party back free movement? It’s a festering dispute inside the party. Its 2017 manifesto committed to ending free movement, and many MPs feel it’s necessary to avoid antagonising immigration-sceptical, often Leave-voting Labour voters in marginal seats. But a majority of the party’s membership base think that free movement has benefited Britain and that its abolition would be an unjustifiable rollback of migrant rights.

So it’s not surprising that the leadership has been inconsistent and indecisive on the question. The arrival of the government’s immigration bill – the legislative instrument that will end free movement – raised the temperature. Labour initially proposed abstaining on the bill at its second reading in January but reversed course after a social media backlash. Now the wound has been reopened by the leadership’s decision to whip in favour of the cross-party ‘Common Market 2.0’ – which would include a barely-modified version of free movement – at last week’s indicative votes, prompting more than 50 MPs to rebel.

Some commentators have tried to sift the record of Labour statements and figure out what the leadership’s true position is. There are hints that make it very tempting to think there’s a secret plan here – Diane Abbott frequently emphasises that the trade relationship with the EU will come before anything else in immigration policy, for example.

But indulging in Kremlinology is mostly a recipe for embarrassment. And, more importantly, there’s a simpler explanation. Labour is hard to pin down on immigration because they haven’t yet admitted to themselves that supporting free movement is the only way it can deliver on its stated goals for migration policy and for Brexit.

Take Abbott’s speech on Labour’s new immigration system last September. She promised a migration policy that would “automatically” allow anyone with a job offer to come to the UK, would not feature a salary threshold and which would not tie migrants’ visas to a particular employer. By far the easiest way to deliver on that promise is a light-touch, liberal system very much like the existing free movement rules.

Apart from the particular proposal, the issues Abbott and her colleagues draw attention also point in the direction of support for free movement. The UK faces not only skills shortages, Abbott rightly points out, but also labour shortages in vital areas like social care and construction. The current rules for non-EU migrants, Labour politicians have repeatedly said in speeches and in Parliament, involve unfair fees, arcane bureaucracy and the cruel separation of families. Abrupt changes to immigration rules and complex residency requirements – like those the new immigration bill would inflict on EU citizens – are exactly what led to the Windrush scandal.

There is no way to mitigate these problems that doesn’t effectively replicate free movement. Take labour shortages. Social care and construction would be heavily affected if EU citizens were brought into the current visa system, with its £30,000 salary threshold. That could be avoided by exempting these sectors from the threshold or, as Labour suggests it prefers, taking salary out of the equation altogether in favour of a more holistic assessment of the value of a migrant’s job.

But how can the government make sure migrants stay in a particular job or sector? The main way of achieving this is by tying visas to employers and enforcing these conditions through the hostile environment – both of which Labour has promised to end. It’s an intractable dilemma in theory, but in practice the solution is simple: if EU citizens retain free movement rights, then labour shortages will speak for themselves and migrants will continue to fill vital social care, nursing and construction jobs as much as they’re needed. It’s a bold step. But it’s also the only way of delivering the immigration policy Labour says it wants.

Or consider the government’s plans, outlined in last year’s immigration white paper, for a 12-month temporary work visa for lower-skilled workers. That suggestion has been roundly opposed by Labour politicians. At the second reading of the immigration bill, the shadow home secretary condemned it as leading to “a huge churn in the workforce” and “a category of second-class workers with no rights who are open to unscrupulous exploitation”, in comments echoed by other opposition MPs.

As we explored in our report on the immigration white paper, there are various ways of reducing the risk of exploitation and harms to integration that the short-term visa would create. To make it more attractive and less risky for both migrants and employers, the policy would need to move towards a longer time limit, the right to bring family members and the opportunity to transfer to other types of visa, rather than being forced to leave the country, at the end of the period.

Those are the kinds of changes Labour might support, based on its objections to the short-term visa proposal. But without exception these modifications are improvements because they approximate free movement rules – which give by far the best package of rights to allow migrants to switch between working and studying, live together with their families and avoid having life disrupted by immigration bureaucracy. This broad set of rights is what protects migrants against exploitation and allows them to integrate comfortably into life in the UK. When Labour makes its arguments against the short-term visa route, they are – knowingly or not – making the case for free movement.

Almost everything Labour’s MPs and shadow ministers say about immigration, and every criticism they make of the government’s approach, implies that free movement is the policy they should want. The party hasn’t yet been willing to acknowledge this. But the immigration bill is proceeding through parliament and crucial Brexit choices are becoming unavoidable. It’s high time for Labour to be open and proud about supporting free movement – the only immigration policy its values can support.