The BBC licence fee should become a voluntary charge, the Match of the Day presenter Gary Lineker says, in comments that are likely to cause dismay at the national broadcaster as it faces a battle with the government over its future.

Lineker, the highest-paid BBC star with earnings from the corporation of £1.75m in 2018-19, told the Guardian the licence fee was the broadcaster’s “fundamental problem” and in need of reform.

“You’re forced to pay it if you want a TV, and therefore it’s a tax,” he said of the £154.50 annual charge on every household watching live television. “The public pay our salaries, so everyone is a target.”

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Lineker suggested the fee – which is currently enforced through the criminal courts - should become voluntary and be charged at higher rate to subsidise elderly and poorer viewers: “I would make the licence fee voluntary. I’ve always said for a long time, I would make it voluntary. I don’t know the logistics of how it would work.

“You would lose some people, but at the same time you’d up the price a bit. It’s the price of a cup of coffee a week at the moment. If you put it up you could help older people, or those that can’t afford it.”

Downing Street is already looking at decriminalising non-payment of the licence fee – a decision that could cost the broadcaster hundreds of millions of pounds in funding. The current licence fee system is guaranteed to exist for the next seven years, although last week BBC director general Tony Hall announced he would quit to allow his successor to negotiate the amount it can charge viewers from 2022 onwards.

The BBC’s news operation is also preparing to announce deep cuts to leading programmes on Wednesday in a bid to make millions of pounds of cost savings. The corporation has already confirmed plans to scrap the award-winning Victoria Derbyshire show, while substantial redundancies are on the cards. Lineker is in negotiations about a new pay deal, with the BBC repeatedly saying his salary was below the market rate for leading football pundits on commercial rivals.

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Lineker, who also presents Champions League coverage for BT Sport, prefaced his comments by praising the BBC as “unbelievably respected around the world” despite criticism of parts of its news coverage from both left and right during last year’s general election. “The BBC is something that I am genuinely passionate about,” Lineker said. “I’ve worked with them for 25 years. And I think it’s something we should be proud of in this country.”

Lineker told the Guardian: “It’s really difficult for the BBC. They are the standard bearer and balance is difficult. Both the right wing and the left wing complain like mad that the BBC are biased. The truth is the BBC is full of thousands of people with varying political views. To say the BBC is fundamentally leftist, or fundamentally rightist, is wrong. It’s been a difficult time because of Brexit and people have been very tribal.”

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In the run-up to Brexit this week Lineker, an outspoken Remainer, says the “lies” of the Leave campaign, exaggerating Britain’s subsidy to the EU, made him despair. But he says the Remain campaign was “too negative”.

“I find it difficult to comprehend,” he said. “But it’s [Brexit] a done deal, so get on with it now. I don’t tweet about it any more. Some people keep going on about it – but I’m not going to bother saying: ‘I told you so.’”

On football, Lineker hails the current Liverpool and Manchester City teams and admits that teams of his era would be thrashed by current sides. And he reveals he has been consulted by football’s rule-making body, the International Football Association Board, about the use of VAR. Lineker is supportive of the principle and critical of the practice.

Had VAR been in place in 1986, Lineker muses, Diego Maradona’s “Hand of God” goal would have been disallowed and England would have beaten Argentina.