The Rolling Stones have waived their claim on royalties from the cover version of You Can’t Always Get What You Want that is being released in memory of the murdered MP Jo Cox.

The track, which features Ricky Wilson of the Kaiser Chiefs, KT Tunstall, David Gray, Steve Harley of Cockney Rebel, and the cross-party parliamentary band MP4, is intended to raise money for the Jo Cox Foundation.

The Scottish National party’s leader in the House of Commons, Pete Wishart – who formerly played keyboard in the band Runrig, and now plays in MP4 – revealed during business questions in the Commons on Thursday that the Stones had offered to forgo their royalties.

“I’m sure the leader of the house would also like to join me in thanking Sir Mick Jagger and Keith Richards for waiving their royalties to their piece of You Can’t Always Get What You Want, ensuring that even more money goes to the Jo Cox Foundation,” he said.

The bookmakers William Hill will donate the money staked on the single being Christmas No 1 to charity. MPs praised the move and urged other bookies to do the same.

Labour MP Kevin Brennan, MP4’s guitarist, said: “Instead of the traditional adjournment debate, perhaps the Tuesday debate could be on a substantive motion in tribute to our fallen colleague Jo Cox, that this House believes we have more in common that that which divides us.

“And if we did have such a debate it would enable us to highlight wonderful gestures like William Hill, the bookmakers, have made this morning around the Friends of Jo Cox single in saying they will donate all the money staked on it becoming Christmas number one, and in addition make a £5,000 donation to the Jo Cox Foundation.

“Does the leader agree that it would be a wonderful gesture if all the other bookmakers matched William Hill’s generosity?”

The Labour leader, Jeremy Corbyn, used prime minister’s questions on Wednesday to urge all MPs to download the single, prompting agreement from the prime minister, Theresa May.

“The right honourable gentleman is absolutely right, we should send a very clear message: download this single for the Jo Cox Foundation, it’s a very important cause,” she said.

“We all recognise that Jo Cox was a very fine member of this House … it’s right, I think, that the chancellor of the exchequer is waiving the VAT on this single. Everybody involved gave their services for free. Once again let’s just encourage everyone to download this single.”

Jo Cox was murdered in Birstall in West Yorkshire, part of her Batley and Spen constituency, on 16 June. Thomas Mair was convicted of her murder on 23 November and sentenced to life imprisonment. The foundation was set up “to advance the values and causes that Jo fought for in her life”.