In written evidence published by the Commons Foreign Affairs Committee, an official working in Lord Goldsmith’s office said the “PM has just authorised” Nowzad “staff and animals to be evacuated”.
Mr Johnson, asked by reporters on December 7 if he had intervened in the evacuation last summer, called the suggestion “complete nonsense”.
Former Royal Marine Paul “Pen” Farthing, who ran the Nowzad shelter, launched a high-profile campaign to get his staff and animals out of Afghanistan after the fall of Kabul, using a plane funded through donations.
The UK Government sponsored clearance for the charter flight, leading to allegations that animals had been prioritised over people in the rescue effort.
The evidence published on Wednesday shows Lord Goldsmith’s official in the Foreign Office emailed colleagues working on the “special cases team Bronze”, saying that other animal welfare charities were looking for assistance after Nowzad had been approved for evacuation.
The official in the minister’s private office wrote on August 25: “[animal charity – name redacted] are a [details redacted] animal charity operating in Kabul and seeking to evacuation their [details redacted] members of staff (no animals).
“Equivalent charity Nowzad, run by an ex-Royal Marine, has received a lot of publicity and the PM has just authorised their staff and animals to be evacuated, [animal charity – name redacted] are hoping to be treated in the same capacity.”
The evidence was submitted to the committee by Raphael Marshall, who worked for the Foreign Office at the time and has claimed that the animals were evacuated following a direct instruction from Mr Johnson.
Downing Street distanced Mr Johnson from involvement in the decision on evacuating the Nowzad animals, when asked about the claims on Wednesday.
The Prime Minister’s official spokesman said: “It remains the case that the PM didn’t instruct officials to take any particular course of action.”
But Dominic Dyer, who led the political lobbying campaign from the UK for Nowzad to be evacuated, said the Prime Minister’s refusal to acknowledge his role in the evacuation had “tarnished” the campaign.
Mr Dyer said the emails published by the committee “vindicated” what he had previously said and argued Mr Johnson could be “very proud of giving support to this as a humanitarian rescue mission”.
He told PA news agency: “I’m not certain why he didn’t feel he could explain his involvement in August at the end of this operation.
“I don’t know why, and I don’t know why this was allowed to turn into such a big political football, for the Ministry of Defence to fall out with the Foreign Office and for Downing Street to say it had no role in it.
“It has tarnished what has been a very important operation that had huge public support, and I think that’s a sad indictment of our political system at the moment, which the Prime Minister presides over to be quite frank.”
Politically, the Prime Minister has been accused of “lying” about his hand in the evacuation.
Labour’s shadow defence secretary John Healey said: “Once again, the Prime Minister has been caught out lying about what he has been doing and deciding.
“He should never have given priority to flying animals out of Afghanistan while Afghans who worked for our armed forces were left behind.
“In this case people were fleeing in terror as the Taliban took over Kabul and British Forces were putting their lives at risk, the Prime Minister was once again prioritising the wrong things and making the wrong calls.
“We need to know why the PM overruled the Defence Secretary with this decision.“
Liberal Democrat foreign affairs spokeswoman Layla Moran called for Mr Johnson to “immediately make a public statement to correct the record and for once tell the truth”.