Foreign Secretary Dominic Raab confirmed the deaths and said a further two people were injured in the attack, which US officials now believe to have been one blast at Kabul airport on Thursday, rather than the originally suspected two.
Mr Raab said: "I was deeply saddened to learn that two British nationals and the child of another British national were killed by yesterday's terror attack, with two more injured.
"These were innocent people and it is a tragedy that as they sought to bring their loved ones to safety in the UK they were murdered by cowardly terrorists."
Mr Raab added: "Yesterday's despicable attack underlines the dangers facing those in Afghanistan and reinforces why we are doing all we can to get people out. We are offering consular support to their families.
"We will not turn our backs on those who look to us in their hour of need, and we will never be cowed by terrorists."
Watch: It is believed ISIS-K carried out the attack at Kabul airport – but who are the group?
As well as the British casualties, officials have said at least 13 US service personnel and 60 Afghan nationals were killed – and more than 150 people were injured – in a "complex attack" on Thursday.
However, both Boris Johnson and Joe Biden have vowed to continue the evacuation effort in Afghanistan despite the attack.
The Pentagon on Friday said it had incorrectly reported that there had been two bombings in Kabul.
Major General Hank Taylor of the Pentagon's Joint Staff told reporters that it is now believed there was no attack at the Baron's Hotel, where processing was taking place.
He said that the US military report was incorrect and attributed the mistake to confusion in the aftermath of the violence.
Earlier, Defence Secretary Ben Wallace said the UK evacuation mission effort out of Kabul had entered its final stages.
About 1,000 British troops, plus RAF aircraft, have been deployed to Kabul airport to help evacuate UK nationals and eligible Afghans.
Mr Wallace also warned that the threat from terror groups will only "grow the closer we get to leaving" following the attack at Kabul airport, believed to have been carried out by the ISIS-K affiliate of so-called Islamic State.
Despite airlifting nearly 14,000 people out of Afghanistan in the past two weeks, Mr Wallace said "the sad fact is not every single one will get out".
He declined to give a timeline for the exit of British forces as they processed approximately a further 1,000 evacuees already in the airport but acknowledged it would come before the Americans withdraw, with Mr Biden having set the departure deadline of Tuesday.
Mr Wallace said the Baron Hotel processing centre was closed at 04:30am, as was the Abbey Gate to Hamid Karzai International Airport.
"We will process the people that we've brought with us, the 1,000 people approximately in the airfield now, and we will seek a way to continue to find a few people in the crowds where we can, but overall the main processing is now closed and we have a matter of hours," he told Sky News.
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Cover image: Explosion site near the Kabul airport in Afghanistan (Picture: Xinhua/Alamy Stock Photo).