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British Home Secretary Priti Patel has said the government will offer a pathway for up to 20,000 Afghans to move to safety in the UK, but that it will take time for the process to benefit the women and children most in need of sanctuary.
On Wednesday, she revealed details of the resettlement initiative for Afghans that offers an initial 5,000 places in the first year.
Ms Patel was forced to defend criticism of the limited numbers of refugees being allowed into the UK, claiming the country cannot house them all "in one go".
"We have to ensure we have the support structures throughout the United Kingdom. We will be working with local councils throughout the country, the devolved governments as well," she said.
"We are working quickly on this. We cannot accommodate 20,000 people all in one go. Currently we are bringing back almost 1,000 people a day.
"This is an enormous effort. We can't do this on our own. We have to work together."
Ms Patel said the UK had been flying people out of Afghanistan since Taliban fighters seized control of the country.
"We have been getting out approximately 1,000 people, so far, a day," she told the BBC. "We're still bringing out British nationals ... and those Afghan nationals who are part of our locally employed scheme."
On Wednesday, UK Prime Minister Boris Johnson told an extraordinary session of parliament that Britain's "core mission" to stabilise Afghanistan after 9/11 had been successful.
Mr Johnson said more than 150,000 British soldiers had served in the conflict and that "sacrifice in Afghanistan is seared into our national conscience".
"The heroism and tireless work of our armed forces contributed to national elections, as well as the promotion and protection of human rights and equalities in a way that many in Afghanistan had not previously known," he said.
He said the UK would judge the Taliban regime by "its actions rather than by its words".
"Defending human rights will remain of the highest priority," Mr Johnson told politicians.
"We will use every available political and diplomatic means to ensure that those human rights remain at the top of the international agenda."
Mr Johnson faced criticism from his own backbenchers, including former prime minister Theresa May, who said the UK's lack of support for Afghanistan was incomprehensible.
She said the crisis was a major setback for British policy and claimed the Taliban takeover of Kabul would embolden those who "wish to impose their way of life on others".
"We all understand the importance of American support but I do find it incomprehensible and worrying that the UK was not able to bring together an alternative alliance of countries to continue to provide the support necessary to sustain a government in Afghanistan," she said.
"Sadly, the life of women and girls will not be the same, they will not have the rights that they should have and they will not have the freedoms that they should have."
Meanwhile, the leader of the opposition Labour Party, Sir Keir Starmer, said the decision to admit only 5,000 Afghan refugees over the next year was based on "a number without rationale".
He said the UK government appeared "ill-prepared and unwilling" to help the people of Afghanistan.
Sir Iain Duncan Smith, a former leader of the Conservative Party, criticised the "shameful" scenes in Kabul and said there was no need for such a "precipitous" military withdrawal.
"The chaotic, ghastly departure – the way that people were falling off the aircraft in their determination to get away – says terrible things about the values that we hold, and those who we wish to protect," she said.
"So this is a shame on all of us, not just America, but also the whole of Nato, and here for us in this house."
Mr Duncan Smith, who previously served with the British Army in Northern Ireland, said US President Joe Biden's recent criticism of the Afghan security forces would become infamous.
More than 70,000 Afghan soldiers had been killed in the fight against the Taliban over the past two decades, many of whom had been trained by British and US forces, Mr Duncan Smith said.
"These men and women have lost their lives in trying to uphold what we had brought to Afghanistan, and we should be proud of them," he said.
"And I do say to the American president, even though the government is perhaps reluctant to say this and even the opposition leadership, you have no right to use excuses and base them on people who have lost their lives, and done so bravely."
Tom Tugendhat, chairman of the UK's Foreign Affairs Committee and a veteran of the war in Afghanistan, said the sight of the Taliban seizing control of Kabul had "torn open some wounds".
"Like many veterans, this last week has been one that has seen me struggle through anger, grief and rage," he said.
“The feeling of abandonment of not just a country but the sacrifice that my friends made.
"I've watched good men go into the earth, taking with them a part of me, a part of all of us. This week has torn open some of those wounds, left them raw.
"What does it say about us as a country about our willingness to defend our values if we are entirely dependent on a unilateral decision taken by the United States?
“This is a harsh lesson for all of us and if we’re not careful it could be a very, very difficult lesson for our allies."
Tobias Ellwood, chairman of the Defence Select Committee, issued a warning about the potential threats from Afghanistan’s collapse.
“I speak with utter disbelief at seeing us make such an utter strategic blunder by retreating at this time," he said.
“A decision that is already triggering a humanitarian disaster, a migrant crisis not seen since the Second World War, and a cultural change in rights to women. And once again, turning Afghanistan into a breeding ground for terrorism."
About 900 British troops have been sent back to the Afghan capital to help repatriate thousands of UK citizens, including embassy staff, after the militants seized power.
The UK said priority would be given to those most at risk, including Afghan women, children and others forced to flee or who were facing persecution from the hardliners.
They should be offered a chance to remain in Britain indefinitely, it said.
"This resettlement scheme will be kept under further review for future years, with up to a total of 20,000 in the long term," the Home Office said.
In the debate Labour lawmaker Chris Bryant called for the programme to be accelerated, asking: "What are the (other) 15,000 meant to do? Hang around and wait until they've been executed?"
The scheme is modelled on that which resettled 20,000 refugees from the Syria conflict from 2014.
Britain was one of the US's strongest allies in president George W Bush's "war on terror", launched after 9/11.
In the southern Afghan province of Helmand, Britain had 9,500 personnel and 137 bases. More than 450 troops died.
But senior politicians and military commanders condemned the peace deal brokered by former US president Donald Trump that led to the withdrawal of foreign forces and gave the Taliban the chance to return, almost unopposed.
The UK said it was working with foreign allies, including in the "Five Eyes" intelligence partnership with the US, Canada, Australia and New Zealand, to identify those most at risk, even as Taliban leaders promised an amnesty and not to take revenge.
Mr Johnson wants an urgent meeting of G7 leaders to stop Afghanistan descending into a humanitarian disaster.
He called for a "unified approach" and increased aid funding.
"We owe a debt of gratitude to all those who have worked with us to make Afghanistan a better place over the past 20 years," he said.
"Many of them, particularly women, are now in urgent need of our help."
Ms Patel, whose family fled to Britain from Uganda during the rule of Idi Amin, earlier said the Afghan Citizens' Resettlement Scheme "will save lives".
"Our country has a proud history of offering sanctuary to those in need," she said.
"We will not abandon people who have been forced to flee their homes and are now living in terror of what might come next."
Britain has come under fire for cutting its foreign aid budget and tightening immigration rules after it left the EU, including for migrants, many of them from conflict hot spots, crossing the Channel from France.
It also faced pressure to provide more help to resettle Afghan interpreters who helped the military after the Taliban were ousted in late 2001.
The latest announcement is separate from that scheme, which expects to relocate 5,000 former staff and their families by the end of this year. Two thousand have already arrived.
Since Saturday, the eve of the Taliban's capture of Kabul, 520 British citizens, diplomats and former Afghan staff have left Afghanistan on military flights, the Home Office said.