Downing Street refused to field a Cabinet minister on BBC1's Question Time this week because the panel featured former Labour spin doctor Alastair Campbell, the flagship current affairs programme said.
Gavin Allen, the show's executive editor, said Number 10 had offered to put up a senior minister but only if Mr Campbell was replaced by a member of the shadow cabinet.
"It is a fundamental principle of our independence that politicians cannot dictate who sits on the panel," he wrote in a blog post this evening.
"It is for Question Time, not for political parties, to make judgments about impartiality and to determine who is invited to appear in the interests of the audience.
"Parties are free of course to accept or reject those invitations, but they do not have a right of veto over other panellists. Licence fee payers rightly insist that the BBC must be free from political interference."
The Tories were represented on the panel for last night's programme by John Redwood, a backbench MP who only this week demonstrated his independence from the Government by voicing his opposition to its plans to increase capital gains tax.
Susan Kramer, a former MP who lost her seat on May 6, appeared for the Liberal Democrats. The other panellists were journalists Piers Morgan and Max Hastings.
It is believed that David Laws, the chief secretary to the Treasury, had been due to appear on the show for the government.
Mr Allen said: "No 10 stated that the objection to Alastair Campbell was that he was not an elected Labour representative or a frontbencher.
"Not only is Alastair Campbell one of the most senior and influential figures in the Labour movement - an architect of New Labour - but Labour ministers regularly appeared on Question Time panels when the then opposition was represented either by someone outside of the front bench or by an unelected panellist - sometimes even a prospective Parliamentary candidate.
"It is not an argument or an objection that bears scrutiny."
Mr Campbell accused the coalition Government of trying to "bully" the BBC and said not having a senior minister on in the week of the Queen's Speech "made a mockery of the Cameron-Clegg claims to be promoting a new politics of engagement".
He also taunted Downing Street's new communications director Andy Coulson for being "totally incompetent". Mr Campbell was himself communications director under Tony Blair.
"I was genuinely surprised - and so was the audience - when David Dimbleby announced that the Government refused to field a minister unless I was not on the panel. I thought I was supposed to be the control freak," Mr Campbell said.
"This pathetic ploy to bully the BBC suggests that the ministers are a bunch of wimps and the Downing Street communications director is totally incompetent.
"I often found Question Time uncomfortable viewing when doing that job but the idea of not having a senior minister in the week of the Queen's Speech makes a mockery of the Cameron-Clegg claims to be promoting a new politics of engagement."
Shadow culture secretary Ben Bradshaw said: "It's extraordinary that in the week of its first Queen's Speech the Government refused to put up a Cabinet minister to explain its policies on Question Time because Alastair Campbell was appearing.
"This curious decision comes in a week which has seen major government announcements on cuts, the Queen's Speech and welfare either leaked to the press or announced outside the scrutiny of Parliament.
"Along with their plans to pack the Lords with new Tory and Liberal peers and the dodgy 55% rule, the coalition's talk of new politics sounds more and more like the politics of a dim and distant past."
A Downing Street spokeswoman said: "In the week of the Queen's Speech the BBC booked Alastair Campbell in the place of an Opposition frontbencher to appear on Question Time - which we questioned.
"Before a final decision was made on who might appear on behalf of the Government, the BBC directly booked John Redwood MP to appear."