One of Britain's wealthiest hedge fund managers, a music producer who is a close friend of Robbie Williams, and a successful author can all be named today as donors to the Hacked Off campaign.

Arpad Busson, whose personal fortune is estimated at £145m, donated £20,000 to the group which is campaigning for new press laws. Other donors include Guy Chambers, a producer for former Take That singer Williams, and the science writer and TV producer Simon Singh, the Observer has discovered.

Hacked Off, which sat in on late-night talks at Ed Miliband's Commons office when the royal charter on newspaper regulation was agreed by the three political parties, refuses to reveal its donors.

On its website, the only funding it discloses is a £50,000 grant during 2012-13 from the Joseph Rowntree Reform Trust and more than £20,000 it says it is due to receive from the Journalism Foundation, a charitable body set up by the owners of The Independent newspapers.

The site also says that actor Hugh Grant will be passing on the damages he receives from his legal action against News International for hacking his mobile phone voicemails.

Last week heiress Jemima Khan confirmed that she had donated £5,000 to the group.

Busson, who had two children with model Elle Macpherson and is married to the actress Uma Thurman, gave £20,000, according to a well-placed source. The French-born financier, who founded the Ark academy of schools, did not respond to queries, but he is understood to have long been a keen supporter of the goals of the group, fronted by Grant.

Chambers, a songwriter, musician and record producer, with whom Williams said recently he is working on a "big project", donated £1,000. His agent did not respond to queries.

Singh, a mathematics and science specialist, whose books include The Code Book, about the history of cryptography, and Trick or Treatment? Alternative Medicine on Trial, also donated £1,000. Singh said he made the donation because he believed the group was fighting for free speech. Singh, who was unsuccessfully sued in 2008 by the British Chiropractic Association for criticising its activities in the Guardian, said fellow campaigners for libel reform were also involved in the group and that encouraged him to give. He said: "It is about getting the balance right between free speech and a responsible press."

Hacked Off and its executive director, Professor Brian Cathcart, have been criticised for the lack of transparency over funding. At a recent literary festival debate, Cathcart was reportedly rounded on when he refused to identify the financial backers of the group.

Audience members shouted "Answer the question!" at him when he was urged to name donors.

However, a Hacked Off spokesman said: "We do not regret accepting money to fund our activities from some people who do not want their donations made public. We understand and respect their desire to avoid the kind of hostile treatment dished out to people who openly criticise the press, and we are grateful to them for their generosity.

"These donations, along with those given publicly, enable Hacked Off to operate on a budget which is a tiny fraction of the funds available to the powerful owners of newspapers."