Boris Johnson rejects the idea of a blanket ban on lucrative second jobs for MPs but believes they must be “visible” to their constituents, No 10 has said. In what appeared to be an implied criticism of the Conservative MP Geoffrey Cox, a spokesperson for the prime minister said he “thinks an MP’s primary job is to serve their constituents”. The intervention came as Cox, who is a former attorney general, was criticised for being paid £150,000 for working for a month in the British Virgin Islands (BVI) during lockdown. In his second job as a lawyer, the Torridge and West Devon MP advised the Caribbean tax haven in relation to corruption charges brought by the Foreign Office. The Daily Mail reported that Cox spent up to a month in the BVI working for the international law firm Withers. At the time, when he was working 4,000 miles away from his Devon constituency, Cox voted in the Commons by proxy. Cox’s register of interests entry shows he is being paid £400,000 a year by Withers law firm, and Labour has called on Johnson to disavow his extra work that it says is taking time away from representing constituents. Johnson’s spokesperson said on Tuesday it was “incumbent on MPs to be visible: to demonstrate to constituents that they are active on behalf of them”. Asked whether Cox had failed to act in that way, he said, “it is up to constituents to make that judgment”. Asked whether there should be changes to the rules on what extra earnings MPs can have from work outside parliament, he said it would be a matter for parliament, but “the prime minister doesn’t back an outright ban on second jobs”. In a fresh shift of position in the parliamentary standards crisis, the government will table a motion to be voted on next week rescinding last week’s moves to protect Owen Paterson. “It will rescind the committee that was part of the amendment and allow the house to vote on the report,” Johnson’s spokesperson said, referring to the standards committee report on Paterson’s conduct. The spokesperson repeatedly declined to say whether the prime minister was sorry about last week’s attempt to protect Paterson from censure over paid lobbying. He said: “We fully recognise the strong feelings on this issue on both sides of the house; the government has been listening carefully to the concerns raised and has expressed regret over the mistakes made last week.” Steve Barclay, the Cabinet Office minister sent to defend the government over its handling of the sleaze row, had also avoided apologising, saying only that it was a matter of “regret”. Meanwhile, Chris Bryant, the chair of the standards committee, announced he had appointed a “senior judicial figure” to advise on potential reforms to the system that investigates allegations of rule-breaking against MPs. He said he was confident the current practice “guarantees a fair hearing”, but that the committee would “consider suggestions for improvement”. Anneliese Dodds, Labour’s chair, has written to Johnson about the latest revelations concerning Cox, and said his “behaviour raises serious questions about the conflicts of interest between MPs having second jobs that involve them lobbying or otherwise directly engaging with the government”. “It’s time to show leadership,” she said. “In fact, it’s past time – you should have come to the House of Commons yesterday to answer questions, apologise and act to clean up the sleaze that is drowning your party and toxifying public life.” Johnson dodged an emergency debate in parliament on his botched bid to save Paterson by ripping up existing anti-sleaze rules, instead saying he had a longstanding engagement at a hospital in Northumberland – where he was seen not wearing a mask while meeting medical staff. Dodds said it was incredible Cox had voted “by proxy from the other side of the Atlantic” and added: “The irony is not lost on me that he arrived in the Caribbean on the day that those MPs who actually feel a sense of duty to their constituents were debating global anti-corruption standards. The people of Torridge and West Devon must be wondering if Geoffrey Cox is a Caribbean-based barrister or a Conservative MP.” Cox’s office has been contacted for comment.