The UK held talks with the Taliban on Tuesday to secure safe passage out of Afghanistan for the British citizens and Afghans in its employ who were left behind when its evacuation mission ended last Saturday.
The government said the prime minister's special representative for Afghan transition, Simon Gass, had travelled to Doha in Qatar to meet senior Taliban representatives.
Mr Gass would "underline the importance of safe passage out of Afghanistan for British nationals, and those Afghans who have worked with us over the past 20 years".
The need for the Taliban's co-operation was made clear by UK Foreign Minister Dominic Raab earlier in the day as he acknowledged it would be challenging for those left behind to return to Britain.
Part of his concern stems from a distrust that the Taliban will stick to its "explicit assurances" on safe passage or be able to run Kabul's airport safely.
"Of course, the previous government had air traffic controllers and things like that," Mr Raab told Sky News. "But at what stage that will be ready and viable for international travel at this point is unclear."
The lack of a stable airport base also exacerbated the challenges of establishing the eligibility of "largely undocumented" UK nationals.
If that can be established, Mr Raab encouraged travelling to third countries with whom the UK is negotiating.
"We've now put in place the arrangements with third countries, or we're putting them in place," he said.
"I've spoken to some of the key third countries, so have other ministers, to make sure we can have a workable route through for those outstanding cases."
"Pakistan or one of the 'stans" had embassies to which the displaced UK nationals should head, Mr Raab said.
The precise number of UK nationals left behind in Afghanistan remains contentious. Some estimates have placed it in the high hundreds, even thousands, but Mr Raab said it was in the "low hundreds".
More than 17,000 British nationals, Afghans who worked with the UK, and other vulnerable people have been moved out of the country since April, he said.
Britain on Wednesday unveiled plans to integrate the new arrivals by offering them immediate full-time residency. It usually takes five years to become eligible for this.
A package nicknamed "Operation Warm Welcome" will see Afghans offered English teaching, extra school places and support with getting healthcare in the UK.
"I am determined that we give them and their families the support they need to rebuild their lives here in the UK," Prime Minister Boris Johnson said.
The residency offer is for those who helped British forces during the 20-year campaign. Ministers have yet to reveal whether it will be extended to those admitted under a wider resettlement scheme.
Taliban special forces at Kabul's airport - in pictures