Afghans seeking refuge in the UK who arrive on small boats from across the Channel will be treated the same as any other migrants who enter the country by the same means, the home secretary has suggested.

Priti Patel appeared to confirm there would be no exception made for those fleeing the Taliban who used “irregular” routes to come to the UK, saying those allowed to resettle in Britain would have to come through one of two schemes.

The first is the new programme launched overnight, which the government says will allow 20,000 Afghan refugees to come to the UK over the next five years and “start a new life in safety”. It will run separately to the Afghan relocations and assistance policy (Arap), launched in April, which offers relocation for those who aided British operations in the country.

Patel said the aim was not to “criminalise” Afghan refugees. But when asked on BBC Radio 4’s Today programme whether they would be treated any differently from other migrants arriving in the UK on small boats, she said: “They will claim asylum in the way in which people who enter our system are currently claiming asylum.”

She continued: “We would obviously tell people not to come through illegal means. Illegal means also means that they’re travelling through many safe countries.

“Irregular migration doesn’t just manifest in the UK, people are travelling through European countries – they can claim asylum in European countries.”

The UK’s chief of the defence staff, Gen Sir Nick Carter, said the Taliban were cooperating with British troops around Kabul airport and were not behaving in “a medieval way”. “They are keeping the streets of Kabul very safe and indeed very calm. They are helping us at the airport,” he told Sky news.

He added that he did not think the Taliban “want to become international pariahs again”, adding: “I do think that they have changed.”

Patel said France “needs to do more” to ensure people claim asylum there rather than continuing on to reach the UK and prolonging their “dangerous journeys”.

While the government’s new resettlement programme has been roundly welcomed, charities have said it will come too late to help those in urgent danger.

Steve Valdez-Symonds, refugee and migrant rights director at Amnesty International UK, said the programme was “unforgivably slow” and not “focused on the most immediate emergency for people at risk in the country”.

He asked: “And what, meanwhile, about Afghans who make their own way to the UK to seek asylum or who are already here? Will they still be vilified and criminalised by the government’s draconian new asylum measures?”

Tim Naor Hilton, chief executive of Refugee Action, said Afghans arriving in the UK through routes other than the resettlement programmes would “be met with punishment, not protection” under the nationality and borders bill – which he called the “anti-refugee bill” – making its way through parliament.

Patel also defended the number of people the government has said will be helped over five years, in the wake of criticism from people including former child refugee and Labour peer Alf Dubs.

Ahead of a five-hour debate in parliament, which has been recalled from summer recess and interrupted the holidays of the prime minister, Boris Johnson, and the foreign secretary, Dominic Raab, she said: “We cannot accommodate 20,000 people all in one go.”

Patel could not clarify whether it would be weeks or months before the first people to be resettled under the new programme arrived in the UK.

She said those who are accepted under the scheme will get housing, welfare support and job and employment help, allowing them to start a new life in the UK permanently.

Earlier, the mayor of Greater Manchester, Andy Burnham, said the Home Office should force all councils to help accommodate those Afghans who are granted refugee status in the UK.