Thousands of people eligible to come to the UK face an uncertain fate as the British evacuation from Kabul draws to a close, with some describing fury and fear at being abandoned to the Taliban in a “hugely mismanaged” rescue effort.

UK ministers have conceded that at least 1,100 Afghan nationals will not be removed in time, but some MPs say this is a vast underestimate of the true number left vulnerable to the new regime and a deteriorating security situation.

“That figure is a fraction of the total sum and a further slap in the face for the brave Afghans prepared to work with the UK for two decades,” said one MP, Labour’s Neil Coyle.

Concern was heightened after the UK announced it had shut its processing centre in Kabul early on Friday, leaving the defence secretary, Ben Wallace, to admit “with deep regret” that many British citizens and Afghans who had worked with the UK were unable to leave.

Thousands of Afghans still congregated outside the city’s airport in a last desperate attempt to force their way on to one of the few remaining flights out of the country, despite a bomb and gun attack on Thursday that killed at least 90 people.

On Friday, the foreign secretary, Dominic Raab, said two UK nationals and the teenage child of another were confirmed as among those who had died, while a UK adult and a child with a British family were injured.

The prime minister said the deaths underlined the urgency of concluding Operation Pitting – the operation to evacuate British nationals and eligible Afghans.

“Of course, as we come down to the final hours of the operation there will sadly be people who haven’t got through, people who might qualify,” Boris Johnson said. “What I would say to them is that we will shift heaven and earth to help them get out, we will do whatever we can in the second phase.”

On Friday night, the government released a letter to MPs stressing its commitment to helping those left in Afghanistan to get out in the longer term under a proposed resettlement scheme. However, it gave no details as to how this might happen beyond saying the UK would emphasise the need for safe passage with the Taliban.

The formal ending of a UK airlift that will have eventually evacuated more than 14,000 people from the country began at 4.30am UK time on Friday, when British forces took a final 1,000 people into the airport for processing, pulling all staff out of a hotel near the blast site where this had been happening.

Wallace refused to say when the last flights would leave but said the timetable had not been changed by the attack claimed by Islamic State. He said the only factor was the need for UK forces and officials to leave before the final American withdrawal on 31 August.

While Johnson has insisted the “vast majority” of eligible people have been flown out, the numbers are unclear, and his characterisation is contested by a number of groups, not least MPs helping constituents with families still in Afghanistan.

The figure of about 1,000 refers to people eligible to leave under the Afghan relocations and assistance policy (Arap), including their families. But the picture for UK nationals and for Afghans eligible to leave in other ways remains much less clear.

Coyle said even the 1,000 figure was “total balls”. He said: “I’ve got written parliamentary questions down on the number of Afghans who’ve helped UK forces, charities and diplomatic effort and it’ll be massive.”

Coyle, who represents Bermondsey and Old Southwark in south London, said that of 52 cases he was dealing with, only four had seen any progress, and almost all involved multiple people, adding: “The number left behind will be in the many thousands.”

Yasmin Qureshi, the Labour MP for Bolton South East and a former UN lawyer, said Wallace’s estimate appeared “completely wrong”, saying a constituent had four family members who had served in the Afghan army and in the police, who were in hiding and unable to get to Kabul or even apply to the Arap programme.

A number of other MPs involved in such cases have given a similar picture, many saying that UK government email addresses to which constituents are told to send details of people needing help almost never give a response.

One Labour frontbencher said they had heard “nothing back” from the government on cases they had sought help for. “We’re not being given updates or anything to tell them, it’s like it’s all just getting sucked into an information black hole at the Foreign Office,” they said.

Those remaining in Afghanistan are being advised to try to cross a land border and reach one of the “processing hubs” in neighbouring countries, a particularly difficult ask given Taliban orders that people should not try to leave.

The operation to get people out of the country is being led by a crisis centre in the basement of the Foreign Office, with more than 100 staff, including military, Home Office and immigration officials, working in shifts 24 hours a day. As the evacuation ends, this will be replaced by longer-term efforts to help those still in Afghanistan.

But many stuck in Kabul say they feel abandoned, and were increasingly hopeless about the possibility of getting back to their homes in the UK, with one telling the Guardian the evacuation operation had been “hugely mismanaged” and a “shambles”.

All said they were increasingly concerned about their safety, and echoed the MPs’ complaints about a lack of official help. They said it had become impossible to get through to the Foreign Office’s Afghanistan helpline and said emails to the dedicated Afghan assistance account were not being answered.

One British citizen said he had spent the past two days hiding in a basement: “We think the Taliban are searching house to house, targeting anyone with a foreign passport. I’m scared for my life. I hope the Foreign Office contact me soon.”

With the 31 August deadline for any final evacuation flights out of Kabul, there has also been a surge of Afghans heading to the Pakistan border, with local officials saying the numbers fleeing are at “unprecedented levels”. The UN refugee agency has said up to half a million people could flee.