Labour will table a vote in parliament on Tuesday calling for the release of documents relating to the UK government’s Rwanda deportation policy amid claims from Conservative centrists that Rishi Sunak has promised to uphold international treaties. The vote, which will be part of a humble address on the opposition day debate in the Commons, will ask for any documents that show the cost of relocating each individual asylum seeker to Rwanda as well as a list of all payments made or scheduled to be made to Rwanda’s government. It will also ask for the UK government’s internal breakdown of the more than 35,000 asylum decisions made last year and an unredacted copy of the confidential memorandum of understanding ministers reached with the east African country. The shadow home secretary said the government’s refusal to “come clean” on the cost of the Rwanda scheme was “totally unacceptable”. “The Conservatives should stop dragging out this chaos and come clean about the real costs and problems,” Yvette Cooper said. “So far, costs are apparently rising to £400m of taxpayers’ money with more home secretaries than asylum seekers sent to Kigali and it is only likely to cover less than 1% of those arriving in the UK.” Labour’s move will seek to accentuate Conservative splits over the safety of the Rwanda bill, a piece of legislation Sunak hopes will prevent further legal challenges to the policy, which will return to the Commons next week. In an interview with the New Statesman that will concern the Tory right, Damian Green, the chair of the centrist One Nation grouping, said Sunak had given personal reassurances that he would not block all appeals or breach international laws such as the European convention on human rights. “The prime minister looked me in the eye and said that he doesn’t want to go any further,” Green told the magazine. “The prime minister’s got within an inch of what I would regard as acceptable. “Almost all our members voted for a second reading with the clear message of ‘thus far and no further’ and ‘don’t take that extra inch’, which some colleagues on the right of the party want us to do.” MPs will consider the bill on 16 and 17 January, the Commons leader, Penny Mordaunt, said on Tuesday. The BBC on Sunday said it had seen No 10 papers from March 2022, a month before the Rwanda plan was announced by the then prime minister, Boris Johnson, which showed Sunak had doubts over the impact of deporting people to Kigali. The documents suggest he was also concerned about the cost of sending asylum seekers to Africa and wanted to limit the numbers. On Monday, Sunak stressed the importance of the Rwanda policy and claimed he had never said he was going to axe the policy but did not deny considering it. He said: “I didn’t say I was going to scrap it. I mean, that’s completely false. Of course I didn’t.” Sunak said it was his job as the chancellor at the time “to ask some probing questions” and scrutinise money spent on taxpayers’ behalf. But ultimately he backed the policy “because I believe in this scheme”, the Tory leader said, stressing the need for a “deterrent” for illegal immigration. Critics on the right of the Conservative party have threatened to amend or even vote down the legislation if it is not tightened before it is next put before MPs. Sunak said he would welcome “bright ideas” on how to improve the bill, while saying “my entire party is supportive” of the legislation.