The UK government intends to get controversial and much-delayed legislation to send undocumented migrants to Rwanda through parliament early next week, Prime Minister Rishi Sunak's spokesperson said on Thursday.

Parliament's two chambers are engaged in a standoff over the proposed law, which Sunak says will deter asylum seekers from crossing the Channel from France in small boats.

The unelected House of Lords again failed to approve the bill on Wednesday, sending it back to the lower House of Commons for a fourth round of legislative to-and-fro.

"It is obviously frustrating that the bill did not pass," Sunak's spokesperson told reporters.

"Our intention now is to get this done on Monday," he said, adding: "We don't want to see anymore delay."

The legislation is the British leader's answer to a Supreme Court ruling last year that sending migrants to Rwanda was illegal under international law.

The new bill would compel judges to regard the east African nation as a safe third country and gives ministers the power to disregard sections of international and British human rights law.

The spokesperson predicted MPs will reject two amendments sought by the Lords when the Commons considers them on Monday.

One seeks exemption from deportation for people who worked with the UK military overseas, such as Afghan interpreters.

The other asks that an independent monitor be established to determine whether Rwanda is in fact safe.

Members of the Lords are expected to concede defeat at some point, recognising that roles are limited to scrutinising legislation and proposing amendments.

Once the legislation is passed, it only becomes law after receiving royal assent.

The deportation proposal has been mired in controversy and legal battles since Boris Johnson unveiled it when he was prime minister in 2022. So far no migrants have been sent to Rwanda.

More than 120,000 people have crossed the Channel on rudimentary vessels since 2018, when the government started recording numbers. Dozens have died, according to monitors.

Even if the law is passed, it is not clear when flights will take off. Charities have vowed to file legal challenges while the government has failed to find an airline willing to take part.

Sunak hopes the scheme will turn around disastrous poll ratings before a general election due this year.

The main opposition Labour Party, tipped to form the next government, has branded the scheme "a gimmick".