In a letter to Mark Thompson, the BBC Director-General, Hammersmith and Fulham Council called on the corporation to move the programme from Television Centre, in White City, West London, over fears that thousands of protesters will picket the building. In a letter, the council demanded that the BBC foot the bill for extra security if it refuses to relocate.

Baroness Warsi, the Tory spokeswoman for community cohesion and social action, is to join the panel on October 22, The Times understands. She is set to appear alongside Bonnie Greer, the black writer and broadcaster, Jack Straw, the Justice Secretary, and Chris Huhne, the Liberal Democrat home affairs spokesman.

Unite Against Fascism, which regularly demonstrates against the BNP, has said that it will try to blockade Television Centre to prevent Mr Griffin gaining access next Thursday.

Demonstrators also plan to hand out leaflets to BBC workers as they arrive at the building in the morning, urging them to stop work for the day in protest.

The Metropolitan Police expects up to 1,000 protesters to descend on the area and is considering using the controversial “containment” tactic that was deployed against G20 activists earlier this year to hem in the crowds. The cost of policing the event could run to tens of thousands of pounds. Lyn Carpenter, director of residents’ services at Hammersmith and Fulham Council, wrote: “A major demonstration, prompted by your programme, represents a significant threat to public safety and, inevitably, it will be our residents whose lives are most adversely affected. The council does not feel that the TV Centre on Wood Lane is an appropriate venue, given the circumstances.

“In light of these issues, I would be grateful if you would clarify what action the BBC intends to take, at its own expense, to mitigate the impact of its decision to film this Question Time programme in the borough. I am also requesting that you consider moving the event to a less urban venue where a major demonstration is more manageable and will have less impact on local residents.”

The BBC is near Westfield Shopping Centre and on an arterial route. The council is also concerned that a mass public protest will bring significant potential disruption to traffic.

Greg Smith, Hammersmith and Fulham’s cabinet member for crime, said that the local taxpayer should not have to pay for the BBC’s decision.

“By putting Nick Griffin in their studio, they are going to cause a problem outside it,” he said. “They have to put up resources and security to ensure that our residents and visitors are protected.”

The BBC will reply to the council this morning, and is expected to tell the local authority that there is “zero prospect” of it contributing to policing costs.

The corporation is well versed in dealing with threats to its headquarters, which was bombed by the Real IRA in 2001, and Question Time regularly hosts high-profile politicians, with tight security details.

The corporation insists that it is required to treat the BNP as a legitimate political party after it won two seats in the European elections earlier this year. A spokesman said: “We are aware of the potential security issues. The appropriate arrangements are being made.”