Rishi Sunak has said he is “determined” to get his Rwanda legislation through Parliament, as ministers prepare for stiff resistance in the House of Lords to the flagship asylum policy.

Many peers have already expressed deep unease about the plan, with ministers braced for a battle with the Upper House over the Bill.

The Prime Minister, who has urged the Lords not to block the “will of the people”, said he wanted to get the scheme “up and running” as soon as possible.

Peers could seriously frustrate that ambition, with Downing Street likely to face attempts by peers to introduce a range of amendments to the proposed legislation.

Former Scottish Tory leader Baroness Ruth Davidson cast doubt policy will ever see asylum seekers deported to east Africa, telling BBC Radio 4 there “are dogs in the street that know” that deportation flights are “probably never going to happen”.

The Bill is likely to receive its second reading by the end of January, with February 12, 14 and 19 pencilled in for debate at the committee stage.

It is possible that the third reading of the Bill could happen around the middle of March.

Mr Sunak played down the prospect of having to pack the Lords with Tory peers to get the legislation through, adding that the country was fed up with the “merry-go-round” on the issue.

Speaking to reporters in Hampshire, he told the PA news agency: “We shouldn’t be talking about these things because the House of Lords will be able to see that this is part of the strong majority in the Commons, they can see that this is a national priority.

“And I would urge them strongly to crack on with it because we all just want to get this done.”

The visit in south-east England came a day after the Prime Minister endured a tumultuous week in Westminster after a significant cohort of Tory MPs rebelled to back amendments to the Rwanda Bill before largely folding and agreeing to back the plan in a crunch third reading vote.

Mr Sunak told broadcasters during a visit to Hampshire: “I am pleased our plan is working and that we’re making progress.

“The numbers last year were down by over a third, that hasn’t happened before, so that shows that we can make a difference here.

“In order to fully solve this problem we need to have a deterrent, so that when people come here illegally they won’t be able to stay and will be removed.

“That is why the Rwanda scheme is so important, and that’s why I’m determined to get it through Parliament and get it up and running as quickly as possible so we can properly solve this problem.

“We have got a plan, this plan is working, if we stick with it we can deliver the change people want to see.”

Mr Sunak has made the Rwanda policy – first proposed in 2022 while Boris Johnson was in Number 10 – central to his premiership, forming part of his pledge to stop small boats of migrants from coming to Britain over the English Channel.

Under the plan, migrants who cross the Channel in small boats could be sent to Rwanda rather than being allowed to seek asylum in the UK.

The legislation, along with a recently signed treaty with Kigali, is aimed at ensuring the scheme is legally watertight after a Supreme Court ruling against it last year.

In a separate blow to the plan this week by peers, the House of Lords International Agreements Committee said that safeguards in the treaty with Kigali are “incomplete”, do not overcome concerns of judges and should not be ratified by Parliament.

A Downing Street spokeswoman said ministers would “consider issues that are raised — motions and amendments — in the usual way”.

“In terms of the improvements and the assurances that we have with the government of Rwanda, we are confident that there will be implementation of all of those measures in line with the timelines for the treaty,” they added.

“So those assurances that we provided, which responded to issues raised by the Supreme Court, will be in place when we get flights off the ground.”

Mr Sunak will hope to have flights in the air ahead of the next general election, expected to be called in the second half of the year.

The Tories, who have promised to “stop the boats”, are expected to make illegal migration a crunch issue in the campaign as Labour remains far ahead in the polls.

But renewed Tory divisions over the Rwanda plan, with both moderate and right-wing MPs criticising Mr Sunak’s strategy, have seen the Prime Minister face fresh questions about his leadership.