Defence Secretary Grant Shapps has said Gary Lineker should stick to TV and questioned whether the Match of the Day host should continue expressing political views.

Former England footballer Lineker was among a group of celebrities to sign a letter which calls for the Government to scrap its Rwanda scheme and for political leaders to come up with a “fair new plan for refugees”.

The high-profile signatories, which also include Succession star Brian Cox, branded Britain’s refugee system “ever-more uncaring, chaotic and costly”, and said asylum policies are not working.

Football pundit Lineker, 63, has previously been at the centre of a BBC impartiality row after he voiced criticism of a Government Bill on the treatment of asylum seekers earlier this year.

He was briefly asked by the BBC to take a step back from Match Of The Day but returned after other stars boycotted the show in solidarity.

The scandal led to the BBC strengthening social media guidelines for staff on issues of impartiality and civility.

Asked if Lineker should express such views while working for the BBC, Mr Shapps told Times Radio: “No. And he’s been through all of this before. The BBC have told him he shouldn’t do this type of thing but still it continues.

“The point I would make to Mr Lineker is: what is right or moral about having people trafficked dangerously across the English Channel, losing their lives at sea, illegally entering the country? That is not a civilised, morally correct thing to do.”

He added: “I just fundamentally disagree with him. What happens to him next is up to the BBC.

“As far as I see it, they have issued previous warnings to him, so it’ll be interesting to see what they do and say at this point.

“I know millions of people watch him for his football commentary and TV presenting, I would have thought it’s better to stick with that.”

The correspondence, also signed by women’s rights campaigner Helen Pankhurst, Hotel Rwanda star Sophie Okonedo and television chef Big Zuu, who is the son of a refugee from Sierra Leone, comes in the week MPs will debate and vote on the Safety of Rwanda (Asylum and Immigration) Bill.

The Government hopes to rush emergency legislation through Parliament declaring Rwanda a safe destination for asylum seekers, after the Supreme Court last month ruled against the scheme.

The letter, co-ordinated by campaign coalition Together With Refugees, stated: “Our Government is still trying to banish people fleeing persecution to Rwanda despite the highest court in the land ruling the scheme unlawful.

“Tens of thousands of people are stuck in limbo waiting for their refugee protection to be processed, separated from their families and barred from working.

We need a new system that reflects the will of the British people who have opened their homes, donated and volunteered in their local communities

“These policies aren’t working for refugees and they aren’t working for local communities.

“That’s why we have come together to say we’ve had enough. Enough of the division. Enough of the short-term thinking. Enough of the wasted human potential. And it’s why we now call for something better.”

Signatories said they are “calling on you, our political leaders of all parties, to commit to a fair new plan for refugees” which includes upholding the UK’s commitment under international law to the right to claim asylum and scrapping the Rwanda scheme.

The letter, marking the launch of the coalition’s Fair Begins Here campaign, also urged a “proper strategy for welcoming and integrating refugees” through “fair, rapid decisions on their application for asylum” and stronger global co-operation “to tackle the root causes that force people to flee their homes and provides positive solutions when they do, including through safe routes to refugee protection”.

Together With Refugees said polling has shown less than a fifth (18%) of people think the Government’s approach to the asylum system is working well, rising to just over a quarter (28%) of respondents who intend to vote Conservative at the next election.

Overall, 83% of the 1,014 adult respondents to the Focaldata polling from last week said they want an asylum system that is well managed, fair and compassionate.

Former England footballer Lineker, who has been outspoken on the issue of the Government’s attitude to refugees, said: “We need a new system that reflects the will of the British people who have opened their homes, donated and volunteered in their local communities.

“That’s why I’m backing this new campaign – because fair really can begin here.”

Responding to Mr Shapps’ criticism of Lineker, a BBC spokesperson said: “Like all freelance presenters, Gary is free to contribute to projects for third parties, as long as these do not conflict with his BBC commitments; do not breach guidelines on conflicts of interest; nor bring the BBC into disrepute, and he does so regularly.”

Another signatory of the letter, former head of the British Army Lord Dannatt, said the “dogged pursuit of the unpopular plan to send people seeking protection to Rwanda is astonishing” and described a “failure to fully support Afghans fleeing the Taliban” as “shameful”.

Big Zuu said his personal experience makes the issue especially important to him.

He said: “I know what it’s like to be a child in the asylum system in the UK. Me and my mum had some good support when we were first here, but it wasn’t easy.

“I know it’s even tougher today, being a refugee in this country now is almost impossible. But it doesn’t have to be like this.

“Being part of this campaign is so important to me and many of the people I grew up with. We experienced the reality and we know politicians can do better.”