Andy Burnham’s call for the UK to consider a return to free movement with Europe has been backed by senior cabinet ministers but risked a rift with “red wall” Labour MPs, who say it could jeopardise Brexit-voting seats.

The prime minister made his plea for an “honest discussion” about freedom of movement in an interview with the Sunday Times, making clear that staying out of it would no longer be a red line in talks with the EU.

Burnham also revealed his belief that rejoining the single market and accepting free movement could be done without the need for another referendum, if Labour put it in their manifesto. In contrast, he said fully rejoining would need another in-out poll.

The prime minister said: “Freedom of movement had very significant challenges associated with it and I spoke about them in my previous time in parliament. But, at the same time, it was a type of immigration that perhaps wasn’t as difficult [as now].

“Revolving-door migration where people would come and then go back is different.…