The UK defence secretary has admitted “some people will not get back” as Britain tries to evacuate Afghan allies from Kabul, along with its own citizens, with British forces aiming to repatriate more than 1,000 people a day.

Ben Wallace appeared to hold back tears as he spoke about the effort to repatriate Britons and process visas for Afghan interpreters and other staff following the Taliban takeover. About 4,000 British nationals and eligible Afghans are thought to be in the capital in need of rescue, with western forces having secured Kabul airport to prepare for their passage out of the country.

Wallace said it was a “really deep part of regret for me” that it would not be possible to extract all Afghans eligible to come to the UK, and many would have to make asylum applications after the evacuation, possibly from third countries.

Wallace’s comments came as British troops arrived in Afghanistan to help evacuate remaining UK nationals and local allies. Paratroopers from the 16 Air Assault Brigade were working with US forces to secure Kabul airport on Monday to ensure flights could continue as Afghans and foreigners scrambled to leave.

On Sunday, Boris Johnson would not put a figure on how many refugees the UK would take from Afghanistan, but Wallace said he was very hopeful that many would be allowed to come to the UK.

A former soldier, the defence secretary has expressed more regret than Johnson and other members of the cabinet over the situation in Afghanistan.

Last week, he criticised the US decision to leave Afghanistan as a mistake that had handed the Taliban momentum. In contrast, Johnson has defended the US position and suggested it was a foregone conclusion that the Taliban would take over, arguing the west had completed its mission of reducing the threat from al-Qaida.

Speaking on LBC radio, Wallace said the situation was “sad and the west has done what it’s done”, adding: “We have to do our very best to get people out and stand by our obligations and 20 years of sacrifice is what it is.”

The defence secretary told BBC Breakfast the Taliban takeover was a “failure of the international community”. He said the evacuation had to be speeded up from its previous timetable of getting everyone out by the end of August. He said the block was not about capacity on planes, but processing speed.

There had been reports that the UK ambassador to Afghanistan, Sir Laurie Bristow, was due to be airlifted out of the country over the weekend, but on Sunday he remained in Kabul airport personally signing visa applications.

Dominic Raab, the foreign secretary, has been criticised for remaining on holiday in Cyprus while the crisis unfolded; he flew back on Sunday. Wallace said he had spoken to Raab daily throughout the effort to evacuate people from Kabul.

He added: “We put in over 600 forces yesterday, today and over the weekend to make sure that we can keep a secure part of the airport functioning and, at the same time, to effectively process, manage and escort people on to our flights to get them out of Afghanistan.”

Asked if Britain and Nato would return to Afghanistan, Wallace said: “That’s not on the cards that we’re going to go back.”

Johnson has also said there is no longer a military solution to the problem.