Britain will press the UN to issue its key demands to the Taliban on Monday as world powers look to continue extracting people from Afghanistan and prevent terrorists using the country as a base.
A draft resolution pushed by Britain, France and the US would tell the Taliban to promise safe passage for evacuees, combat terrorism and ensure that humanitarian staff can safely work in Afghanistan.
A meeting of UN ambassadors from the five permanent Security Council members - the UK, US, France, Russia and China - will take place later on Monday.
UK diplomatic sources said that Britain planned to work with Russia and China given their potential ability to influence the Taliban and shared interest in preventing a refugee or drugs crisis.
The draft resolution was negotiated over the weekend. French President Emmanuel Macron revealed to a Sunday newspaper that London and Paris hoped to establish a safe zone for evacuations from Kabul.
The final flight in Britain's two-week military airlift left Afghanistan on Saturday, but it intends to keep the door open to Afghans and British nationals by applying pressure on the Taliban.
Estimates of the number of Afghans left behind after the airlift range between 800 and several thousand.
James Cleverly, the UK's Minister for the Middle East and North Africa, said on Monday that it was impossible to give a certain figure. He said many had been evacuated before the fall of Kabul.
"Even though we don’t have access to Kabul airport any more, we’re still negotiating with other countries to look at other routes whereby those who are not able to get to Kabul can perhaps get out of the country by other means," he told LBC radio.
UK Foreign Secretary Dominic Raab will stress the importance of safe passage in talks with G7 nations, Nato, Qatar and Turkey on Monday.
He will say that engagement with the new Afghan regime must take place "on a pragmatic basis, responsive to the actions of the Taliban not just their words," it is understood.
The UK's other priorities are protecting regional stability, holding the Taliban to account on human rights and preventing terrorists from using Afghanistan as a safe haven.
Al Qaeda used the country as a base from which it planned the 9/11 attacks in 2001. Security experts have said that the Taliban takeover could open the door for new training camps in Afghanistan and inspire extremists to take up arms elsewhere.
The "imperative that Afghanistan not be allowed to be used as a base for terrorist attacks" is part of the planned resolution which Barbara Woodward, the UK's envoy to the UN, will discuss with counterparts.
In Doha, UK Prime Minister Boris Johnson's special representative for Afghan transition, Simon Gass, will engage with partners on the same issues.