Following ping-pong yesterday, the Lords backed two amendments and sent the bill back to the Commons, where it will be examined on Monday.

The first amendment insists that Parliament decides whether Rwanda is safe; the second exempts from deportation Afghans who assisted British troops.

Peers voted 245 to 208 in favour of crossbench peer Lord Hope’s amendment that would permit flights to take off only once the home secretary has had the right to review Rwanda’s status as a country safe for refugees.

They agreed to the former lord president and Supreme Court justice’s measure requiring Rwanda to pass independent verification before it was deemed safe.

Lord Hope told peers that his amendment must be added because, as things stand, the home secretary lacks the power to overturn the claim that Rwanda is safe.

“The minister has told you that the government are not obligated by the treaty to send anybody to Rwanda if the facts change,” he said. “That may well be so, but that is not what the bill says. The secretary of state is bound by the statute to ignore any such changes.”

The UK government suffered a further defeat after peers backed by 247 votes to 195 an exemption from removal for those who worked with the military or government overseas, including Afghan interpreters.

Labour peer Lord Coaker said it was “morally bankrupt” of the government not to stop Afghan interpreters from being deported.

The shadow immigration minister, Stephen Kinnock, said: “Neither prime minister nor the home secretary believe this batshit bill will end the chaos the Tories have created in our asylum system.

“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.”