The pair will almost certainly steal the show from the rest of the panel, which will include conventional politicians like Labour's shadow transport secretary Mary Creagh.
What could they come to blows over? HuffPost UK presents five questions that the Ukip leader may be tempted to ask the comedian and activist.
1. "Why do you hate capitalism, a system that made you rich? You even once took money to plug the wares of big business, didn't you?
2. "Why don't you put your money where your mouth is and give some of your fortune to good causes rather than relying on big government?"
[Brand, estimated to be worth £15 million, was asked by the Guardian if he would give away his fortune. His response? "No". But he did add that he was "no longer interested in making money" and would use what he gets "for good".]
3. "Our popularity is growing and most Brits agree with us on leaving the European Union, as a believer in people power, why don't you join the 'People's Army'?"
4. "How come you get to be a radical revolutionary spokesman despite admitting to 'suffering the ol' sexism' and making prank calls to rape hotlines, while I get attacked as a misogynist for suggesting women don't breastfeed 'ostentatiously'?"
5. "Why don't you 'stop talking in riddles about how you'd run the country' and stand for Parliament and help me change it?"