Rishi Sunak has urged peers to “do the right thing” and back his Rwanda legislation as he prepares for a showdown with the House of Lords after winning Commons approval for his illegal migration plan.

The Prime Minister saw his legislation pass its third reading in the Commons on Wednesday night, after a would-be backbench revolt on his Rwanda Bill largely melted away.

But the victory came only after dozens of backbenchers rebelled and two party deputy chairmen quit to back right-wing amendments over the course of Tuesday and Wednesday, in the latest sign of the deep divisions within the party.

He is now facing a major battle with peers in the House of Lords, many of whom have already expressed deep unease about the Rwanda plan.

Ministers have already been warned the flagship policy will face stern opposition from the Lords, with one prominent crossbench peer warning the Bill represents “a step towards totalitarianism”.

Mr Sunak on Thursday insisted his party is “completely united” in support of the policy, as he warned peers against blocking the “will of the people”.

At a press conference in Downing Street, he said: “It’s now time for the Lords to pass this Bill. This is an urgent national priority.

“The treaty with Rwanda is signed and the legislation which deems Rwanda a safe country has been passed unamended in our elected chamber.

“There is now only one question. Will the opposition in the appointed House of Lords try and frustrate the will of the people as expressed by the elected House? Or will they get on board and do the right thing?”

I’m interested in sticking with the plan I set out for the British people because that plan is working

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.

But backbench right-wingers had urged Mr Sunak to toughen up the Bill to sideline Strasbourg judges and ignore any so-called Rule 39 orders from the European Court of Human Rights that would ground flights for asylum seekers.

Number 10 has instead offered new guidance reminding officials to follow any ministerial decisions that would ignore the injunctions, to the anger of civil service trade unions.

Mr Sunak repeated once again that there are circumstances under which he would be prepared to ignore the Rule 39 orders, as he repeatedly insisted his “plan is working”.

But time is running out for Mr Sunak to get flights in the air, with the House of Lords able to significantly stall the Rwanda legislation and put in jeopardy a previous ambition to have removal flights leaving by the spring.

Mr Sunak on Thursday said the timeline is now a matter for the House, as he shared his frustration at delays but failed to guarantee flights would take off by the end of the year.

“Will the House of Lords understand the country’s frustration, see the will of the elected House and move as quickly as we have to support this legislation so we can get it on the statute books and then get flights up and running?” he said.

He told reporters ministers had moved as quickly as possible to get the legislation through the Commons.

“We are not messing around here,” he said.

Reports emerged earlier that some Tory MPs have submitted no confidence letters in Mr Sunak after the parliamentary wrangling of recent days.

Speaking in front of an audience which included Home Secretary James Cleverly and illegal migration minister Michael Tomlinson, Mr Sunak rejected suggestions he is the “wrong man for the job”.

“I’m interested in sticking with the plan I set out for the British people because that plan is working,” he said.

He also downplayed any prospect of the UK seeking a refund from Kigali if the Government fails to send any migrants to the East African country, after Rwanda’s President Paul Kagame appeared to suggest British taxpayers’ money could be repaid if the deal fails.

“I’m fighting every day to get the flights off to Rwanda,” Mr Sunak told reporters.

The stalled policy already comes with a £290 million bill. No asylum seekers arriving by unauthorised routes have been relocated.

More than 600 migrants have now arrived in the UK so far this year after a busy day in the Channel saw 358 people make the crossing in eight boats on Wednesday.

Opposition parties accused the Government of focusing on the Rwanda plan to the detriment of issues such as the struggling NHS and cost-of-living pressures.

The Liberal Democrats said the Tories were “too busy fighting over an unworkable and expensive policy”, and the SNP said Mr Sunak’s priorities were “all wrong”.