Labour has called on the defence secretary, Ben Wallace, to explain how he can reconcile Foreign Office emails saying Boris Johnson authorised a controversial airlift of animals from Kabul in August with his own assertion to MPs earlier this week that this was not the case. A letter sent by John Healey, the shadow defence secretary, pressed Wallace for an explanation hours after peers had demanded a similar explanation from the Foreign Office minister Zac Goldsmith, who also denied that Johnson had approved the rescue in a statement he made to the Lords in December. In the correspondence, Healey asked Wallace: “How do you square” the Foreign Office emails released earlier this week with “the evidence you gave to the foreign affairs select committee”, and he asked again if Johnson had “authorised the evacuation” of animals from Pen Farthing’s Nowzad charity. The defence secretary has repeatedly denied that he was ordered by No 10 to allow Farthing’s evacuation flight to proceed. On Tuesday he told MPs on the select committee that “at no stage, at any stage, did the prime minister ask me to make a way for those pets. Not at all. Never.” A Foreign Office email released on Wednesday showed that an official working for Lord Goldsmith had written to a colleague on 25 August to say “the PM has just authorised” the staff and animals of the Nowzad welfare charity to be cleared for evacuation. The questions to Wallace came after the Labour peer Ray Collins in the Lords asked Goldsmith to reconcile the apparent discrepancy between the August email and a statement made by the junior minister to the house on 7 December. Goldsmith had said rebuttals made by Johnson that same day about his own involvement in authorising the rescue of Nowzad animals were “from my own experience … entirely accurate”. But on Thursday, in light of the email disclosures, Lord Collins asked Goldsmith, who was not present in the Lords, “to return as a matter of urgency to make a statement to the house” to clear up the apparent discrepancy between the email sent from his private office on 25 August and remarks he made months later. The government minister Nicholas True said Goldsmith had tweeted a statement on Wednesday, in which he said: “I did not authorise and do not support anything that would have put animals’ lives ahead of people’s … I never discussed the Nowzad charity or their efforts to evacuate animals with the PM.” Later, Lord True added: “Allegations do not constitute evidence.” Boris Johnson, Downing Street and other ministers have repeatedly denied the prime minister gave his personal permission for a privately funded rescue flight to land in Kabul at the end of August. However, an animal rights campaigner linked to Nowzad, Dominic Dyer, said he believed the prime minister did sanction the rescue. On Thursday, Johnson said “this whole thing is total rhubarb”, and that he was proud of the military’s role in rescuing thousands of people stranded in Kabul after the Taliban’s seizure of Afghanistan’s capital. A day earlier, Labour accused Johnson of lying, after the initial disclosure of the Foreign Office email from Goldsmith’s private office. A second email, sent later on 25 August by another Foreign Office official involved with the Kabul airlift, repeated the point. It said: “In light of the PM’s decision earlier today to evacuate the staff of the Nowzad animal charity … ” Controversy about the rescue of Farthing, a former royal marine, and his charity’s cats and dogs, and the involvement of the prime minister, has lingered for months after Wallace, who previously appeared to not support their evacuation, unexpectedly announced he would allow it in a tweet sent at 1.33am. There was support from some quarters for allowing the animals to be evacuated, but others said that creating a landing slot for the plane when thousands of Afghans were still desperate to be evacuated amounted to a prioritisation of “pets over people”. Supporters of Nowzad engaged in an intense lobbying effort that Dyer said involved Goldsmith. Dyer also said he sent regular updates to the prime minister’s wife, Carrie Johnson, as the crisis unfolded. Farthing and more than 150 cats and dogs were eventually rescued in one of the last flights out of Kabul on a charter plane, but last-minute delays at the airport meant more than 60 Nowzad staff and their dependents had to cross the border to Pakistan before they could be transported to the UK.