Home Secretary James Cleverly accused Labour of a “politically cynical” effort to scupper the Rwanda scheme as peers dealt another blow to the asylum plan.

Labour said the Government should stop wasting time and money on the “hare-brained scheme” which aims to send some asylum seekers on a one-way trip to Rwanda in order to deter people from crossing the English Channel in small boats.

Prime Minister Rishi Sunak has insisted he wants to get flights to Rwanda off the ground this spring but MPs will not consider the legislation again until Monday.

The House of Lords snubbed ministerial calls to back down and again insisted on revisions to the Safety of Rwanda (Asylum and Immigration) Bill.

Mr Cleverly said: “Terrified that the Rwanda scheme will work, and desperate to delay or disrupt over a hundred votes about stopping the boats, Labour have acted again to block the passage of the Rwanda Bill.

“It’s been another politically cynical effort by them, who have no alternative deterrent and no plan to tackle illegal migration, to frustrate the only solution on offer.

“We want to break the criminal people smuggling gangs and stop the boats. Labour, uncomfortable with tackling immigration, will clearly stop at nothing to stop the planes”

But shadow immigration minister Stephen Kinnock said: “More people arrived on small boats in a single day this weekend than will be sent to Rwanda in a year, and yet they’ve committed half a billion pounds of taxpayers’ money to this hare-brained scheme.

“They can try to blame Labour, the Lords, or even the former military leaders who voted to amend the Government’s Bill this evening to prevent Afghan interpreters who helped our armed forces from being sent to Rwanda.

“But this is their mess, and they have no idea how to solve it. Rather than wasting more time and money on their failed scheme they should back Labour’s plan to properly protect our border security and go after the criminal smuggler gangs.”

The fresh Government defeats mean a continuation of wrangling at Westminster over the proposed law that aims to clear the way to put asylum seekers who cross the Channel in small boats on a flight to Kigali.

The Bill and a treaty with Rwanda are intended to prevent further legal challenges to the stalled asylum scheme after the Supreme Court ruled the plan was unlawful.

As well as compelling judges to regard the east African country as safe, it would give ministers the power to ignore emergency injunctions.

Despite MPs overturning previous changes by the upper chamber, peers renewed their demand that Rwanda cannot be treated as a safe country until an independent monitoring body has verified that protections contained in the treaty are implemented.

The provision would also allow the Secretary of State to effectively pull the plug on the scheme if the promised safeguards were not maintained.

In a further blow to the Government, peers again supported an exemption from removal for those who worked with the UK military or Government overseas, such as Afghan interpreters.

The Lords’ insistence on the amendments ensures a fourth round of “ping-pong” over the Bill, where legislation is batted between the two Houses until agreement is reached.

The draft law will be sent back to the Commons, where MPs are set to consider the latest changes on Monday.

Ministers denied suggestions that the Bill was not being rushed through repeated rounds of ping-pong this week because the Government was not ready to get flights off the ground.

Northern Ireland minister Steve Baker told BBC’s Newsnight: “I don’t accept that. The reality is that legislation usually takes months to put through … I’m well aware that at this stage of legislation, when you are in ping-pong between the two houses, things get tense, difficult and you need to very carefully proceed.

“It’s true ping-pong could have gone on through the night, but really we are going to be proceeding within days to come back to ping-pong, I think that’s perfectly reasonable.”

Labour suggested that one reason the Government was trying to buy time was because it is struggling to find any airline willing to carry the asylum seekers.

Mr Kinnock claimed the Government was trying to “scramble high and low” for an airline to be associated with the “unworkable, unaffordable and unlawful” scheme.

The Times reported the Prime Minister could use RAF Voyager aircraft for Rwanda deportation flights after the Home Office failed to find a charter company.