The involvement of Mr Grade is likely to raise eyebrows at the corporation, which he is ultimately responsible for regulating. He already chairs Pinewood Shepperton, the film and TV studio owner, and Hemscott, the financial information company, despite a commitment to work four days a week at the BBC.

A successful bid would place him in the position where another company in which he is involved earns money from the BBC. According to the BBC’s most recent annual report, the corporation paid £640,577 to Pinewood Shepperton for use of its facilities in the year to March 31, 2004.

Mr Grade has teamed up with Michael Linnit, the theatrical agent, to bid for Lord Lloyd-Webber’s Really Useful Group, which manages the composer’s publishing rights and the production of popular musicals such as Evita and The Woman in White.

If they win the auction for the business, which formally kicked off with last Friday’s deadline for first-round offers, it is thought that Mr Linnit would run the company, with Mr Grade acting as non-executive chairman.

Mr Grade, who is understood to be seeking a handful of Lord Lloyd-Webber’s separately owned theatres as part of the deal, has secured backing from Grant Gazdig, a former colleague of Robin Saunders, the City dealmaker. Mr Gazdig left Ms Saunders’s new Clearbrook investment firm in January to set up Access Capital, and an acquistion of the Really Useful Group would mark his first UK deal.

The BBC Chairman also has backing from a mystery wealthy individual, while Royal Bank of Scotland and Barclays have agreed to underwrite the debt component of the leveraged bid.

The Lloyd-Webber estate contains some of the most highly sought-after intellectual property in the theatre world; competition for the assets is likely to be fierce.

Clear Channel Entertainment of the US is thought to be among the keenest competitors in the auction, which Ingenious Capital, the sale’s adviser, hopes to conclude by the end of the summer.

The auction comes less than a week after it emerged that Lord Lloyd-Webber has entered advanced talks to sell his Apollo Shaftesbury, Duchess, Lyric and Garrick theatres in the West End.

The BBC declined to comment.

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