On Monday, BBC Trust chairman Lord Patten said the corporation must "command credibility" in how it dealt with the allegations.
The Conservatives respect the paternalistic ideals of Lord Reith, a founder of the corporation, but are warier of the institution itself.
Mrs Miller has written to the chairman of the BBC Trust, Lord Patten, to stress that the corporation's investigations into itself should be conducted "thoroughly".
The BBC defended Mr Marsh over what the corporation called "implied criticism" from Lord Hutton about an e-mail the editor sent to a senior colleague criticising Mr Gilligan's reporting methods.
Long time critics said it proved that the Corporation is badly run and that its chairman Lord Patten should now face the chop.
But on Tuesday, former director of public prosecutions Lord Macdonald, who reviewed for NI's owner News Corporation the e-mails in a file relating to bribes allegedly paid to police, said they contained "evidence of serious criminal offences".
Despite the corporation's shrill response, the reforms proposed by Lord Carter, the communications minister, are only nudges in a new direction.
Lord Hall said it was time to look at how all the corporation's money was spent while keeping in mind the difficult circumstances the country as a whole was facing.
BBC: New BBC boss Tony Hall vows to tackle senior staff pay-offs
Lord Tomlinson was particularly concerned about Sir Digby reportedly wanting a more competitive corporation tax system - seen as a criticism of Mr Brown's policy.
BBC: NEWS | UK | UK Politics | MPs laugh about 'Comrade Digby'
Update, 15:55: I was fascinated that in the House of Lords debate today, Lord Puttnam said that he believed Jeremy Hunt as culture secretary could intervene to block News Corporation's bid to own all of BSkyB, on the grounds News Corp would not be a "fit-and-proper" owner (in the light of the recent revelations about conduct at the News of the World).
Lord Hall joined the BBC as a news trainee in 1973 and during his 28 year career at the corporation oversaw the launch of Radio 5 live, BBC News 24, the BBC News website and BBC Parliament.
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