Rishi Sunak’s flagship Rwanda deportation bill is expected to be put on hold until at least next month after the House of Lords inflicted seven defeats on Wednesday.

The safety of Rwanda (asylum and immigration) bill, which aims to block Strasbourg from halting the removal of asylum seekers to east Africa, is not expected to return to the Commons until after the Easter break.

Any delay could make it increasingly difficult to fulfil the prime minister’s plan to see flights take off for Kigali by the spring.

The legislation is central to the Conservative government’s pledge to “stop the boats”. Ministers have claimed that the bill will deter people from travelling across the Channel.

In the wake of the defeats, the Labour peer Shami Chakrabarti said: “Given that the prime minister has bet the house on this post-truth bill, these further Lords defeats leave his credibility even more denuded.

“Arguments about the international and domestic rule of law hit home and home is where many Conservative peers seem to have stayed.”

Peers voted by 271 to 228, majority 43, to press their demand that the legislation has “due regard” for domestic and international law; they backed an amendment by 285 to 230 votes that states Rwanda is only deemed to be safe for as long as the provisions of the UK’s treaty are in place; and a linked amendment regarding the monitoring of Rwanda’s safety was also voted through.

Peers voted 276 to 226 in favour of the crossbench peer David Hope’s amendment, which lays out how it is to be decided whether the provisions of the Rwanda treaty are in force. Another amendment, by Lady Chakrabarti – that removes a key clause declaring Rwanda a “safe country” in the decision of individual asylum claims – was voted through by a majority of 30.

The government suffered another defeat when peers backed a change to its Rwanda Bill regarding the age assessment of unaccompanied children.

The bill came back to the Lords after MPs on Monday voted down 10 amendments to the draft law proposed by peers earlier this month. It has to be passed to activate the deal that would allow the UK to send asylum seekers to Rwanda. It has so far cost taxpayers up to £600m and has been signed off by three Conservative prime ministers since 2022.

The bill must return to the Commons in a process known as “ping pong”, where it is batted between the two parliamentary chambers until they can agree the final wording. Labour has suggested it will not seek to block the bill completely.

Before the bill returned to the Lords, the illegal immigration minister Michael Tomlinson described the proposals put forward by peers as “wrecking amendments”.

Another vote is expected to wait until MPs return from their Easter break on 15 April. Sources said the government will not clear the Commons schedule to allow votes next week.

No 10 officials insist that even if the legislation is not passed until after Easter, the goal of the first deportations taking place this spring could still be met.

Yvette Cooper, the shadow home secretary, said the Rwanda scheme is a failing farce, which will only cover less than 1% of asylum arrivals.

“It is clearer than ever that Rishi Sunak knows this plan won’t work and only sees it as a political gimmick to get what the former immigration minister described as ‘symbolic flights off just before an election’.

“If the Conservatives were ready to implement this, they would be bringing the bill back to complete the remaining stages next week and get on with it,” she said. “But because their plans aren’t ready, they’ve decided to delay the bill as well, so they can try to blame everyone else for the chaos they have created.”

As well as suffering defeats in the Lords, Sunak is under pressure from the right of his party after the Home Office said it would pay some asylum seekers thousands of pounds to move to Kigali.

James Cleverly, the home secretary, said: “I am pushing in parliament for a deterrent scheme supported by the Rwandans that will not only help stop the boats but provide a safe destination for those who are in the UK illegally. It’s why we need the Bill through.

“While Labour and their allies try anything to delay, disrupt or destroy that plan, people are risking their lives in the hands of people who don’t care if they die as long as they pay. The talking needs to end so we can get on with the job of saving lives and stopping the boats.”