Andy Burnham is backing Shabana Mahmood’s controversial changes to the immigration system, his allies have said, in a blow to those in Labour who hope to soften them.

The Greater Manchester mayor is understood to be keen to reframe the changes but supportive of the home secretary’s attempts to limit legal and illegal migration, which have been criticised by some senior Labour MPs as un-British and mimicking Trump.

Burnham faces a tough fight to return to Westminster against Reform UK, which has already called him “open-borders Andy”. But those close to his campaign say he will not seek to dilute the government’s curbs on migration, which include ending the right to permanent refugee status.

“For Andy, migration is a moral issue as much as anything, showing people who’ve lost faith in politics that we do have control and we can do good,” one source said.

“We need to tell a positive story about the contribution of migration to our country, but we cannot do that unless people trust that the people they vote for have control over our borders.”

Spokespeople for Burnham and Mahmood declined to comment.

Burnham was confirmed as Labour’s candidate for the Makerfield byelection earlier this week, and is widely expected to seek to run for the party leadership if he wins the seat, either by challenging Keir Starmer or persuading him to step down.

But Labour MPs who have canvassed in the constituency say it will be a very difficult fight in a seat where Reform’s support surged at the local elections.

“Andy is fighting the most important by election in half a century in the Labour-held seat with the largest Reform vote in the country,” a source close to the campaign said.

“Immigration is the second most important issue there. He must show decisive leadership on this and reframe but back the reforms to restore control over our borders and create a firm but fair migration system.”

The Conservatives announced on Wednesday that they would also stand a candidate, Michael Winstanley, despite calls from some prominent Tories to give Reform a free run at the seat in an attempt to defeat Burnham.

With the local campaign barely under way, Burnham’s policy positions are already being picked over by supporters and opponents for signs of what he might do in government.

He backed away from his previous support for the idea of rerejoining the EU earlier this week, saying it was not something he wanted to see in the immediate future.

Many in Labour are now pushing him to make his stance on migration clear, given the scale of the changes that Mahmood is pushing through.

She set out a major package of changes earlier this year that included scrapping permanent refugee status and removing government support from asylum seekers who are deemed not to need it or who break the law. Anyone who has been granted asylum but whose country is then deemed to be safe will be asked to leave.

She also promised to double the length of time it takes for some people to achieve settled status in the UK from five years to 10, a measure which officials say will apply to many already in the country. That is due to come in later this year once the government has completed a consultation on which groups should be exempted from the longer timetable.

Mahmood told the Guardian earlier this year that Labour MPs should back her or risk a government led by Nigel Farage deporting refugees “to certain death”.

Despite her pleas however, many including several key Burnham allies – greeted her proposals with outrage.

Sarah Owen, a leader of the Tribune group of centre-left Labour MPs, said at the time that the idea of deporting children mimicked Trump’s Immigration and Customs Enforcement (ICE) detention of minors in the US.

Angela Rayner, the former deputy prime minister, has called them un-British.

Burnham’s closest allies in the party seem broadly comfortable with his position. In an email to MPs on Wednesday, his team announced that two prominent MPs from the soft left – his close friend Anneliese Midgley and the former transport secretary Louise Haigh, another leading member of Tribune – would run the campaign in Makerfield.

Despite the criticism from prominent MPs, Labour members, who will vote in any future leadership election, are more divided on the issue.

Polling from YouGov published on Wednesday suggested that more than half of party members say they want the same or more restrictive immigration policies. Just 26% said they wanted a more liberal approach, 44% backed Mahmood’s changes and 18% said they would prefer an even tougher approach.

The poll shows roughly half of Labour members believe the party faces a greater risk of losing votes to ReformJust 15% think vote losses to the Greens are the bigger issue, and 27% said both pose an equal threat.

Burnham has previously said he backed changes to the immigration system and especially efforts to reduce the use of asylum hotels.

In an interview with the Guardian’s Politics Weekly podcast last year, he said: “Immigration control has weakened as a result of Brexit. We’ve replaced one form of immigration with a very different form of immigration that is more long-term.”

He has expressed reservations, however, about the idea of reassessing asylum seekers’ status if their home countries become safer for return.

Speaking on the Today programme last year, he said Mahmood was “right to grasp this nettle and have root and branch reform of the system. I agree with that.

“I do have a concern about leaving people without the ability to settle, one of the concerns being if there is a need to constantly check up on the status of countries where people have come from, that might limit the ability of the Home Office to deal with the backlog.”