Britain’s bill for housing asylum seekers will climb to more than £5bn a year by the end of the next parliament as the government’s approach to illegal migration leaves thousands more waiting indefinitely for their case to be handled, according to a report. Adding to the growing pressure on Rishi Sunak to halt small boat crossings of the Channel, the left-leaning Institute for Public Policy Research thinktank said the prime minister’s new Illegal Migration Act was likely to deepen the crisis in the asylum system. The IPPR said there was likely to be a “steadily increasing” number of people who could not be compelled to leave the UK but had no means of securing permission to stay and had no right to work. The report was released hours after Sunak suggested he would not stop small boat crossings by the time of the next election, although he said figures showed a decline compared with last year. Warning that the problem could not be solved overnight, Sunak said: “The current system is both unsustainable and is completely unfair, but particularly unfair on British taxpayers who are forking out millions of pounds to house illegal migrants in hotels and local communities.” In its report, the IPPR said the number of people arriving in small boats had risen rapidly over the past five years, from the hundreds to tens of thousands. With a backlog of 130,000 cases, asylum support costs were already running at £3.5bn a year and are set to rise further. Under the Illegal Migration Act, which was passed by parliament in July, migrants arriving by irregular means – including on small boats – are denied any prospect of a hearing, the thinktank said. As most could not be returned home under international or UK law, those who are not sent to Rwanda or another third country – through a scheme the courts have judged to be unlawful – would find themselves in indefinite limbo. Even on the government’s assumption that it removes 500 people a month to be processed overseas, the annual cost of housing asylum seekers would be more than £5bn within five years. The bill would rise to more than £6bn a year if the number removed reduced to 50 every month. There was little realistic prospect that most of those who arrived by small boat crossings would be removed to a third country, even if the Rwanda plan is eventually ruled lawful, the IPPR said. Marley Morris, associate director for migration, trade and communities at IPPR, said: “Even with the act fully implemented, under most plausible scenarios arrivals will still outpace removals. “This will mean a growing population of people permanently in limbo, putting huge pressure on Home Office accommodation and support systems – plus a risk of thousands of people who vanish from the official system and are at risk of exploitation and destitution. “Any incoming government would be likely to face a dire and increasingly costly challenge which it would need to address urgently from the outset – there will be no option to ignore or sideline the crisis it inherits.” A Home Office spokesperson said: “The Illegal Migration Act will help to clear the asylum backlog by allowing us to detain and swiftly remove those who arrive here illegally. While we operationalise the measures in the act, we continue to remove those with no right to be here through existing powers. “We are also on track to clear the ‘legacy’ backlog of asylum cases. It has been reduced by a nearly a third since the start of December and we have doubled the number of asylum decision makers in post over the past two years.”