He said the judicial review, submitted to the High Court, alleged that three appointments were made without advertising the posts and without the open competition normally required for high-level posts in the public sector.
The case concerns the recruitment of the head of testing and traceability and his conservative counterpart, Baroness Dido Harding; Kate Bingham, head of the UK vaccine task force; and Mike Coupe, director of NHS Test and Trace, added the observer.
Jolyon Maugham QC, director of the Good Law Project, said on social media: “It is our belief that cronyism – which undermines the public interest, discriminates against those who do not rub shoulders with Cabinet ministers and excludes those who lack the family fortune to work unpaid – is illegal.
“And we at @GoodLawProject intend to prove it in court.”
Mr Maughan said the organization would release the full court documents on Sunday.
A spokesperson for No 10 said: “We are not commenting on the ongoing legal proceedings.”
The Good Law Project and the overcrowded Runnymede Trust fundraising page said Lady Harding had just ‘passed the job’ as head of the National Institute for Health Protection without any other candidates being considered.
She said she was not the only one to land a high-level position in this way and that “very often” the people who had been recruited had “personal and political connections with the government”.
He said: “In August, conservative peer Dido Harding was appointed head of the National Institute for Health Protection.
“Wife of a Conservative MP and friend of former Prime Minister David Cameron, Dido Harding did not send other candidates for the post during the interview.
“There were no other candidates. She just got the job.
“She’s not the only one to land a top job this way.
“Every week it seems like another person is performing a role of vital public importance without any publicity or fair process – and very often that person has personal and political connections to government.”
While the page said that naming “your comrades” was not new or “the preserve of the Conservative Party”, it was time to end it.
He added: “This government’s approach discriminates against people born without a silver spoon in their mouth.
“It’s unfair to those who don’t rub shoulders with high-ranking ministers. And that’s unfair to groups that the data shows are excluded from public life.
“Appointing your comrades to high-level positions is not new or the preserve of the Conservative Party: we all remember ‘Tony’s Cronies’ too.
“But it’s high time we put an end to it.
“Runnymede Trust and the Good Law Project are challenging the appointment of Dido Harding, as well as a series of other appointments that were made apparently without any publicity or a fair recruitment process.”