- War in Afghanistan (2001-present)
image sourcePAimage captionAfghan interpreters worked with the Army in Helmand province
Labour has urged the government not to "abandon" Afghan workers who helped British forces by allowing more of them to settle in the UK.
Many interpreters and other former staff are fearing for their lives as the Taliban continues to extend its control over the whole of Afghanistan.
Shadow home secretary Nick Thomas-Symonds said the UK had to put in "specific and safe" asylum routes.
The government has said it should get more than 1,000 people a day to the UK.
Defence Secretary Ben Wallace told the BBC the biggest barrier to increasing the rate of evacuation was not a lack of capacity on planes but "how quickly" people can be processed by officials.
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US forces have secured the perimeter of Kabul airport, where hundreds of Afghan and foreign workers are waiting for flights out.
The UK has also sent around 600 UK troops to assist the withdrawal, with Prime Minister Boris Johnson promising to get "all those who have helped the UK effort over 20 years" out of Afghanistan "as fast as we can".
Labour leader Sir Keir Starmer said all those who had served deserved protection, adding that there should be no "nice distinction" between workers based on their professions or whether they had been UK government employees or contractors.
Mr Thomas-Symonds has written to Home Secretary Priti Patel, asking for an update on the numbers of those being helped.
"The situation in Afghanistan is truly awful," he said. "We must now live up to our obligations, especially to those Afghan people who worked so bravely with British representatives in Afghanistan.
"Our resettlement scheme must urgently be expanded to ensure people to whom we owe a huge debt are not abandoned."
Last week the government said about 2,000 Afghan interpreters and "other people we have an obligation to" would also be transported to the UK, joining about 3,000 who have already been taken out of the country.
Mr Wallace told BBC Breakfast: "Our flights, our planning and coming in and out and soon if we manage to keep it in the way we're planning to, we should have capacity for over 1,000 people a day to exit to the UK.
"Currently this is not about capacity on planes; it's about processing speed. So that's why we're trying to fix that."
Mr Wallace also said the rules had change to allow more contractors who had served British forces into the UK, and that he would speak to the home secretary about further moves to process as many Afghan passport holders as possible.
Downing Street has said plans for wider asylum and any updates to eligibility for the resettlement scheme will be set out in the coming days.
But Mr Wallace added: "There will be some people left behind. We made that clear in the last few weeks. I'm not going to raise expectations."
Ministers would "do our very best" to get those eligible out of Afghanistan by 31 August, he added.
Appearing on LBC radio, Mr Wallace was close to tears as he said that "some people won't get back", adding: "It's sad the West has done what it's done."
As the government scrambles to get people out of Afghanistan ministers are engaged in an exercise of mitigation, as events unfold in Kabul beyond their control.
But they will want to show they have some sort of grip on the crisis, by successfully evacuating British passport holders – and eligible Afghans who've worked with the British authorities.
However as an emotional Defence Secretary today admitted, not everyone will get out.
On refugees, with many Afghans expected to try and flee, Downing Street won't give potential numbers but says it will set out its approach to wider asylum claims in the coming days.
More broadly, the government is still insisting that once the Americans decided to go, it wasn't feasible for the UK to stay and act unilaterally.
But this, as well as Britain's broader approach to foreign policy over the last two decades, will all be up for discussion when Parliament is recalled in on Wednesday – in two days time. That may feel a little late as, in Afghanistan, things seem to be changing hour by hour.
Jack Straw, who was Labour's Foreign Secretary when the allied invasion of Afghanistan happened in 2001, told the BBC News Channel he was "not in any doubt at all" that it had been "entirely the right thing to do in the circumstances".
The Taliban had refused to hand over operatives of the al-Qaeda terror group that it was harbouring in the aftermath of the 11 September attacks on the US, he added.
"A lot of good has happened over the intervening 20 years," Mr Straw said, adding that his "disagreement" was not over "whether" a withdrawal was needed but "how you did that".
Conservative MP Nus Ghani said the government had let down Afghan workers who trusted the UK, asking: "What message are we sending now? Working with us means that we will walk away and you will be slaughtered by the Taliban."
Foreign forces are pulling out of Afghanistan following a deal between the US and the Taliban militants they removed from power in 2001.
The Taliban has pledged not to allow Afghanistan to become a base for terrorists who could threaten the West.