Last night the BBC's chairman, Sir Christopher Bland, issued a stern rebuke to the Tory leader and warned him that the corporation would not be influenced by political pressure "whatever the source".
It also emerged that Mr Hague's letter to Sir Christopher, in which he argued that it would be "totally unacceptable" for Mr Dyke to win the top job, was received by The Times newspaper before it reached the BBC.
Mr Hague faced the further embarrassment of his stance conflicting with that of a potential leadership rival, Michael Portillo, who said Mr Dyke's pounds 50,000 donation to the Labour Party should not bar him from the post.
In a letter to Mr Hague, Mr Bland rejected the Tory leader's claim that the director-general was the "ultimate guarantor" of the impartiality of the BBC.
"It is the board of governors who are the ultimate guarantors of the political impartiality of the BBC ... in appointing the next DG, we will continue to recognise and discharge that responsibility through a vigorous and objective selection process. We will not be influenced by political pressure, whatever the source," he wrote.
One BBC insider added: "The first the BBC press office knew of the letter was when it appeared in the first edition of The Times, which has led the attack on Dyke."
The BBC's press spokesman drew attention to Sir Christopher's established position. "The appointment of the director-general is the responsibility of the governors alone," he said. "There has been and will be no discussion of any candidates with any politicians of any party. The best man or woman for the job will be appointed by the 12 governors, following a vigorous, careful and objective selection process."
Mr Portillo said in The Scotsman newspaper less than a week ago that "civic-minded people" such as Mr Dyke should not be penalised.
"I'd be sorry if successful people were put off contributing to political parties. It's better that a candidate's political opinions be in the open and Mr Dyke knows that he would have to leave them at the entrance to Broadcasting House," he said.
Frank Dobson, the Secretary of State for Health, warned that the Tories themselves had had close links with previous BBC chairmen. Marmaduke Hussey was brother-in-law of the former minister William Waldegrave. Stuart Young, another former BBC chairman, was the brother of the Tory minister Lord Young. "If the Tories start to draw attention to political links of people at the BBC, then they have a lot of explaining to do," Mr Dobson said.
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