Prime Minister Rishi Sunak vowed that nothing would prevent him from sending asylum seekers to Rwanda after parliament finally approved the divisive policy that is designed to deter migrants from travelling in small boats to Britain.

Hours after the bill passed, a French newspaper reported that at least five migrants had died in an attempt to cross the Channel. The French coast guard could not confirm the details but said there were several “lifeless bodies”.

Tens of thousands of migrants – many fleeing wars and poverty in Africa, the Middle East and Asia – have reached Britain in recent years by crossing the English Channel in small boats on risky journeys organised by people-smuggling gangs.

Britain has been seeking for two years to deport some of those arriving in the hope it would stop the flow of migrants, with the government arguing the crossings risk lives and enrich criminal gangs.

“Our focus is to now get flights off the ground, and I am clear that nothing will stand in our way of doing that and saving lives,” Sunak said in a statement.

Once the bill has passed into law – expected later this week – the government will be free to start detaining asylum seekers, a move that will trigger further legal challenges by charities, campaigners and unions who argue that Rwanda is not a safe destination.

Steve Smith, the head of Care4Calais charity which has previously challenged the policy, said it would work tirelessly to block any flights and sought to reassure migrants in Britain.

“They can be assured that Care4Calais will not only stand in solidarity with them, we are absolutely committed to fighting for their safety here in the UK,” he said in a statement.

Stopping the flow is a priority for the government, but critics say the plan to deport people to Rwanda rather than handle asylum seekers at home is inhumane. They cite concerns about the East African country’s own human rights record and the risk asylum seekers may be sent back to countries where they face torture.

Sunak’s new law states some existing UK human rights statutes will not apply to the scheme and Rwanda must be treated by British judges as a safe destination, in a bid to override a Supreme Court ruling which declared the scheme unlawful.

It also limits individuals’ options for an appeal to only exceptional cases.

Sunak said on Monday that the first flights would take off in 10 to 12 weeks’ time. He said an airfield was on standby, slots were booked for flights, 500 staff were ready to escort migrants and courts had been reserved to process appeals.

Charities and rights groups say they will try to stop individual deportations and the trade union which represents border force staff is promising to argue the new legislation is unlawful “within days” of the first asylum seekers being informed they will be sent to Rwanda.