A band of Labour MPs and trade unionists are calling for Jeremy Corbyn to commit to defending free movement when the UK leaves the EU, highlighting the party’s split over the issue.

Clive Lewis, an ally of Corbyn, has joined David Lammy and Geraint Davies in signing a open letter in support of letting UK and other EU citizens continue to live and work across the bloc without barriers.

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Labour’s official position, like the government’s, is that free movement will end at the point of Brexit in March 2019, but it has not backed a particular immigration system to replace it.

Many MPs with seats in Labour’s Brexit-voting heartlands in the north and Midlands are keen for tighter restrictions on immigration to show the party listened to a key message of the EU referendum.

But Corbyn and his shadow home secretary, Diane Abbott, have always been supportive of the aims of free movement of people and have declined to say that immigration overall should fall.

In their open letter, the MPs, national executive members, Momentum organisers and trade unionists, called on Labour to “respond with clarity, humanity and solidarity” on the issue of immigration.

“Migrants are not to blame for falling wages, insecurity, bad housing and overstretched public services,” they said. “These are the product of decades of underinvestment, deregulation, privatisation, and the harshest anti-union laws in Europe. On the contrary, migrant workers have been on the frontline of fighting for better pay and working conditions. Labour is the party of all working people – regardless of where they were born.

“A system of free movement is the best way to protect and advance the interests of all workers, by giving everyone the right to work legally, join a union and stand up to their boss without fear of deportation or destitution. Curtailing those rights, or limiting migrants’ access to public services and benefits, will make it easier for unscrupulous employers to hyper-exploit migrant labour, which in turn undermines the rights and conditions of all workers.”

Michael Chessum, an organiser for the Labour Campaign for Free Movement, said he was concerned that “Labour’s immigration stance has for far too long been dominated by pandering to the idea that immigration is to blame for a fall in living standards”.

He said: “This isn’t just factually wrong, it’s also self-defeating - because we need a narrative that is clear and honest about the fact that neoliberalism and exploitation are the real problem. That has to be backed up with policy, not just sentiment. We beat the Tories when we’re principled and offer alternatives – that’s the lesson of the general election.”

