Alister Jack, the Scottish secretary, has spared Rishi Sunak a byelection by ruling out taking the peerage he is understood to have been offered by Boris Johnson. The Dumfries and Galloway MP, a close ally of the former prime minister, became the latest Conservative to confirm he would stand down from his seat at the next election. Sunak could still face byelections in the constituencies of the former ministers Nadine Dorries, Nigel Adams and Alok Sharma, who are also believed to have put forward by Johnson for the Lords. It is understood that the House of Lords appointments commission, which vets peerages, has advised the Cabinet Office that MPs will have to stand down if they wish to take up a peerage. After a drubbing at the local elections, Downing Street will be keen to avoid any further tests of the Conservatives’ support at the polls, which could undermine Sunak’s authority and even put his premiership at risk. As many as 29 sitting Conservative MPs had already announced they would not be contesting the next general election. They include the Scottish Tory leader, Douglas Ross, younger figures such as the levelling up minister, Dehenna Davison, and veterans such as Graham Brady. Jack said he would definitely not accept the peerage while still sitting as an MP but he left the door open to accepting an honour and entering the Lords after the next election. “I’m not going to the House of Lords and causing a byelection,” he said in an interview with ITV Border. Asked if he would go to the Lords if he stood down at the next election, he replied: “Who knows?” Jack, who was first elected to the Commons in 2017 and served in the administrations of the last three prime ministers, is believed to have been nominated for a peerage in Johnson’s resignation honours list. “I’ve been very clear in saying that I will not be standing at the next general election. I said that to Boris Johnson, I’ve said that to Liz Truss when she appointed me as secretary of state for Scotland,” he said. “And I said it to Rishi Sunak when he also appointed me as secretary of state for Scotland. At each reshuffle, I’ve said: ‘I want to be honest with you, I’m not standing at the next general election.’ But they’ve factored that in and given me the privilege of continuing to serve.” He held his seat in 2019 with a majority of just over 1,800 over the SNP, who had held the seat before 2017. Polling projections suggest Labour would take Sharma’s Reading West seat and Adams’ seat of Selby and Ainsty in the event of byelections. The Tories would be expected to hold on to the Mid Bedfordshire constituency that has been represented by Dorries since 2005. Her majority at the last election was more than 24,000.