The selection of the next BBC chairman will be “an establishment stitch-up”, a senior MP has warned amid growing concern at the cosy relationship between those making the decision.

Britain’s most powerful civil servant, Sir Jeremy Heywood, is helping to choose the next chairman and his wife was handed a £600,000 contract by the BBC Director-General, Lord Hall, to carry out a review of the corporation last year. The review was dubbed “the bonfire of the boards”, but it has been described by BBC insiders as “essentially a waste of money”.

Lord Hall and Lady Heywood are good friends, having worked together at the Royal Opera House, where Lord Hall was chief executive. Lady Heywood sits on the board of directors at the opera house. The BBC said at the time of the review that Lady Heywood had been hired after a “competitive process”.

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Philip Davies, a member of the Commons Media Select Committee, which must approve the trust chairman proposed by Sir Jeremy’s panel before the formal appointment, said: “This is a panel to deliver an establishment stitch-up. This is not the process by which we’re going to end up with a BBC Trust chairman who is going to hold the BBC to account, which is what people look to the chairman to do on behalf of licence payers.”

Last month, it emerged that Lady Hall is a senior employee of the headhunting firm Saxton Bampfylde, which is being paid tens of thousands of pounds to recruit the new BBC Trust chairman. Mr Davies said: “Given that Tony Hall’s wife works for the recruitment firm in charge of this process, and given he is friends with the wife of one of the interview panel, I don’t know why don’t they just go the whole hog and let Tony Hall choose the next chairman.”

He questioned why Sir Jeremy is part of the three-strong interview panel for the £110,000 post, which Lord Patten of Barnes vacated in May. “There’s plenty to be doing trying to reform the civil service. He should be focusing on that, not trying to find some stitch-up for the BBC chairman post as well.”

The core purpose of the chairman is to police the BBC on behalf of licence-fee payers. Sir Jeremy’s involvement in choosing the candidate is regarded as a break with precedent because the Whitehall seat on the panel has previously been filled by a senior staff member from the body overseeing the appointment process, the Department for Culture, Media and Sport (DCMS).

Labour’s Margaret Hodge, who chairs the Commons Public Accounts Committee, said: “The selection process has to be open. This is a particularly important appointment for the BBC, as it tries to restore confidence in itself. Anybody involved in it has to be really careful that they are open about any potential conflict of interest.”

The job description for the role of trust chairman was quietly altered to reduce the time commitment from “three to four” days a week to as little as two days a week if necessary. It has been speculated that this was part of an attempt to lure Lord Coe, believed to be the Government’s preferred candidate, to the job.

A spokesman for the DCMS said: “It is essential the best possible person is appointed and Sir Jeremy Heywood, as the most senior civil servant in the UK, will help ensure the right candidate is identified.”