The BBC has accused the government of political interference after it refused to provide a ministerial guest for Question Time unless Alastair Campbell was removed as a panellist.

BBC executives said they rejected the demand and tonight's show went out without a representative from the coalition government.

Gavin Allen, the show's executive editor, posted a blog on the BBC website saying No 10 had insisted that Tony Blair's former director of communications was replaced by a shadow cabinet member. "Very obviously we refused," Allen wrote, "and as a result no minister appeared, meaning that the government was not represented on the country's most-watched political programme in Queen's speech week – one of the most important moments in the parliamentary calendar." It is understood that the cabinet minister originally pencilled in to appear was David Laws, the chief secretary to the Treasury.

The panel consisted of Campbell, former Liberal Democrat MP Susan Kramer, broadcaster and former newspaper editor Piers Morgan, author and journalist Sir Max Hastings and the Tory MP John Redwood, the former Welsh secretary.

Allen said Downing Street objected to Campbell because he was "not an elected Labour representative or frontbencher". Allen wrote: "This week for the first time in my three years as executive editor of Question Time we were told by Downing Street that a cabinet minister would only appear on the programme if another member of the panel was replaced."

After the programme, which is pre-recorded, had been filmed Campbell wrote on Twitter: "Question Time over. Mystery revealed as to why there was no minister. Govt said would not field if I was the Labour voice. Pathetic."

He had earlier used the social networking site to reveal that Laws had been pulled from the show. "Mugged up on David Laws cos led to believe he was govt minister on Question Time. Turns out there won't be one! In Queen's speech week!"

Allen wrote: "It is a fundamental principle of our independence that politicians cannot dictate who sits on the panel. 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."

Question Time chair David Dimbleby opened the show by saying: "We would have expected to have a government minister..." and revealed to viewers that Downing Street had demanded Campbell's removal. The former Labour spin doctor responded by saying that request was "extraordinary" and added it "made a mockery" of the coalition's claims to represent "the new politics".

Campbell produced a framed photo of Laws and said: "I've brought … the man who should have been here."

The BBC had a difficult relationship with the Tories when they were in opposition. David Cameron sought to freeze the licence fee last year and there is a suspicion among some BBC executives that the Conservatives are intent on curbing its power.

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."

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."