Labour’s divisions over immigration have broken out again after the party’s Brexit spokesman said EU free movement rules “have got to be changed”.

Sir Keir Starmer warned politicians not to ignore the reasons why people voted to leave the European Union, arguing those motivations included curbing immigration.

He said: “There should be a fundamental rethink of immigration rules from start to finish.

“The rules on free movement have got to be changed – or the way the rules operate has got to change.”

Sir Keir also insisted that, within the Labour party, “there is a consensus that, when we leave the EU, the immigration regime will have to change”.

Yet, in an interview only last week, Jeremy Corbyn suggested that the free movement of workers across the EU should continue after Britain’s exit.

The Labour leader also appeared to set himself against calls for EU citizens to be allowed to come to Britain only if they have a job, rather than to seek work.

But, speaking with The Sunday Times, Sir Keir suggested immigrants should be required to have a job, arguing such an idea could form part of a future trade deal with the EU.

“People, when you talk to them about immigration, have a strong distinction in their mind between people who are coming here to work and contribute and those who are coming here to look for work and I think that distinction is well worth exploring,” he said.

Several high-profile Labour figures, including Yvette Cooper, Andy Burnham and Emma Reynolds, have called for their party to accept immigration curbs in the wake of the referendum.

The Brexit spokesman also warned that arguments over triggering the Article 50 exit clause – and over a “hard” or “soft” Brexit – risked failing to address the “deeper issues” behind the referendum result.

“If we just concentrate on the process and fight about the deal with the EU, we leave out half the picture and half the analysis,” he said, adding that immigration, the damage done to public trust by the MPs’ expenses scandal, stagnating wages and job insecurity were among the reasons people voted to leave back in June.

Sir Keir said Labour needed to respond with a “bold and ambitious” ten-year skills and industrial strategy and plans to devolve decision-making to a local level.

“I'm not pretending I have a fully-fledged, spelt-out project for the future, but I have a fair idea of what I think the big ticket items are,” he said.

Sir Keir, the director of public prosecutions for five years before becoming an MP in 2015, is seen by some as a credible future Labour leadership candidate, if Mr Corbyn continues to fail to make progress.