Gary Lineker has said the government should never be involved in appointing the chair of the BBC, after the resignation of the incumbent, Richard Sharp. Sharp announced on Friday he was stepping down after accepting the findings of an independent investigation that said he had breached the rules for public appointments. It said he had failed to declare his role in helping to secure an £800,000 loan to the then prime minister, Boris Johnson. Lineker, who was suspended as Match of the Day presenter last month after the BBC said he had breached its impartiality guidelines, later weighed in on how Sharp’s successor should be chosen. He tweeted: “The BBC chairman should not be selected by the government of the day. Not now, not ever.” Lineker’s suspension caused an unprecedented walkout by his fellow presenters, upending the BBC’s sporting schedule and leading the broadcaster to return Lineker to his role. He refused to apologise for his tweets criticising the government’s asylum policy, one of which described a video by the home secretary, Suella Braverman, about refugee boat crossings as “beyond awful”. When challenged, he responded to another user: “This is just an immeasurably cruel policy directed at the most vulnerable people in language that is not dissimilar to that used by Germany in the 30s, and I’m out of order?” Tim Davie, the BBC’s director general, acknowledged “potential confusion and grey areas” in what presenters were allowed to tweet and promised a review of BBC social media guidelines. This decision was later echoed by the regulator, Ofcom, which said the corporation’s editorial guidelines needed updating for the modern world. But the incident was widely seen as a humiliating own goal for the broadcaster, and greatly increased the pressure on Sharp, a financier and Tory donor, over his links to Johnson and his role in a secret loan to the then prime minister. Labour and the Liberal Democrats said Sharp’s position had become untenable. Lineker, the BBC’s highest-paid presenter, is freelance and his Nazi Germany comments were made on his personal Twitter feed. The remarks, he told a magazine earlier this month, were “factually accurate”, saying he hadn’t been willing to backtrack because they were “fair and true”. In an interview with Men’s Health UK, he said: “I talked about the use of words like ‘invasion’ and ‘swarms’ and ‘criminals’ and ‘rapists’, which I think we should be very careful about because it has real-life consequences. “I wasn’t abusive, I wasn’t saying she [Braverman] was a Nazi,” he said. His tweet on Friday in reaction to Sharp’s resignation prompted a reply from fellow presenter Carol Vorderman, another outspoken critic of the government, who tweeted: “Absolutely.”