MPs and peers are set for a final showdown over the Government’s Rwanda Bill after weeks of parliamentary back-and-forth.

The Government has vowed to keep Parliament sitting late into the night if necessary to pass the Safety of Rwanda (Asylum and Immigration) Bill, which it sees as vital to the Prime Minister’s pledge to “stop the boats”.

Peers have repeatedly blocked the legislation with a series of amendments, stretching debate on the “emergency legislation” over more than four months and delaying flights taking asylum seekers to Rwanda.

Downing Street is hostile to the idea of making concessions to secure the passage of the Bill, setting up a showdown with peers.

The Bill is intended to overcome the objections of the Supreme Court by forcing judges to treat Rwanda as a safe country for asylum seekers and allowing ministers to ignore emergency injunctions from the European Court of Human Rights.

Speaking on Friday, Rishi Sunak said his patience with those blocking the Bill had “run thin”, adding: “No more prevarication, no more delay. We will sit there and vote until it’s done.”

Last week saw peers amend the Bill yet again to include an exemption for Afghan nationals who assisted British troops and a provision meaning Rwanda could not be treated as safe unless it was deemed so by an independent monitoring body.

On Monday, MPs are expected to vote to overturn those changes before sending the Bill back to the House of Lords, where some peers may attempt to insist on their amendments again.

If so, the Bill would return to the Commons late on Monday for a further vote and then return once again to the Lords in a process known as “ping pong” that could last well past the Commons’ usual 10pm finish.

If peers pass exactly the same amendment twice, however, the Commons faces the choice of either accepting the change or losing the Bill under a rarely-used process known as “double insistence”.

Crossbench peer and former independent reviewer of terrorism legislation Lord Anderson has raised this possibility and described the legislation as a “post-truth Bill” that asks Parliament to declare Rwanda is safe when, he argued, it is not.