LONDON - A new law to crack down on migrants arriving in Britain in small boats from Europe across the English Channel will be unveiled on Tuesday, with a senior minister saying "enough is enough", the Sun on Sunday newspaper reported.

The British government has been promising to step up action to tackle the issue after the numbers making the perilous crossing soared to more than 45,000 last year.

The paper reported the proposed new legislation will mean that all those who arrive on small boats will have their asylum claims ruled inadmissible, and will be removed to a 'safe third country' as soon as possible.

"Enough is enough. The British people want this solved," Home Secretary (interior minister Suella Braverman told the paper. "They are sick of tough talk and inadequate action. We must stop the boats."

The number of migrants arriving on the English coast has more than doubled in the last two years and tackling the issue was one of five key priorities outlined in January by Prime Minister Rishi Sunak, whose party is languishing in polls, under pressure from his own lawmakers to find a solution.

Last year, former Prime Minister Boris Johnson agreed a deal to send tens of thousands of migrants, many having made the journey from Afghanistan, Syria or other countries suffering war, more than 4,000 miles away (6,400 km) to Rwanda.

But the first planned deportation flight was blocked in June by a last-minute injunction granted by the European Court of Human Rights (ECHR), and the strategy's lawfulness was subsequently challenged at London's High Court.

London's High Court subsequently ruled it lawful in December, but opponents are seeking to appeal that verdict. It is expected the legal battle will end up in the UK Supreme Court and so may not be resolved for months.

The policy has been denounced by human rights groups and even reportedly by King Charles.

Last November, Sunak agreed a deal with France to step up efforts to address illegal immigration, and he is due to travel to Paris this week for a bilateral meeting when the issue is set to be a major topic of discussion.

(Reporting by Michael Holden, Editing by Louise Heavens)