The One Nation group of centrist Tories is considering tabling amendments to Rishi Sunak’s Rwanda bill to protect the controversial legislation against breaches of international law. Conservative MPs on the party’s moderate wing are concerned the government could cave in to demands from the right to harden the bill to avoid them voting it down in the new year. Former justice secretary Robert Buckland, a member of the One Nation group, is considering tabling an amendment of his own to make the bill legally more safe so it is compatible with the European convention on human rights, the Guardian can reveal. He denied that such an amendment would “wreck” the bill, saying he wanted the prime minister’s Rwanda plan to succeed. “It could get support from across the house, unlike amendments that may be tabled by the right,” he said. “Third reading will be the key test for the government. As for suggestions from colleagues on the right that their amendments would strengthen the bill, I fear they will undermine it by making a direct clash with the courts inevitable.” Other centrist Tory MPs are looking at ways of holding the government to its commitment to remain within international law and prevent Sunak from giving significant concessions to the right. Damian Green, the former deputy prime minister, said that One Nation MPs would only accept “very minor” amendments from the right, as the current bill “goes right to the edge of what is acceptable”. After 29 Tory MPs abstained on the bill on Tuesday, the vast majority from the right of the party, a Common Sense Group source said there was scope to gather the requisite number of votes to oppose the legislation in the new year. They said they could find another “15 or 20 votes” if necessary to switch from voting for the bill to voting against. “There were many members who felt that they had to give the government the benefit of the doubt at an early stage of the bill,” one said. “They won’t be so generous next time unless there is a serious attempt to stop legal action against the Rwanda scheme because we know that as it stands it will get tied up in the courts.” The “five families”, a loose alliance of rightwing Tory groups, expect to go into the new year with further discussions with the government over the bill and how it can be “tightened” to satisfy that wing of the party. “We have a history of looking at legislation productively and creatively,” the source said. One senior rightwing MP who met Sunak before the vote said he had suggested tweaking clause 4 of the bill, which allows migrants to continue lodging individual claims, to add further curbs. The prospect of doing similar deals to the Rwanda deportation scheme with other countries was also discussed. The group has complained that the scope of the bill to disapply elements of human rights law is “very narrow” and does not go far enough to address the risk of the European court of human rights blocking the plan, although any amendment on the issue is likely to antagonise centrists. No 10 said that Sunak would listen to any sensible proposals for amendments to the bill. “The prime minister has been clear that, on the issue of people putting forward amendments, they need to be done in a way that is legally credible, has the deterrent effect and ensures the scheme does not collapse.” However, Alex Chalk, the justice secretary, indicated that the government would not cede to the right by denying asylum seekers any right to appeal, as the bill had to remain “within the four corners” of the UK’s international legal obligations. “We are of course willing to listen to sensible suggestions and insights … However, we do think that there are certain aspects which are important to uphold to ensure that we remain within international law.” Meanwhile, legal migration minister Tom Pursglove has said the government did not want the hike in the income threshold for family visas to apply “retrospectively”. Downing Street has already rowed back on its position on whether the new minimum income rules will apply when existing visas come up for renewal – initially saying they would but then suggesting just days later that had not been decided.