Presenters Matt Edmondson and Mollie King were quizzed by a man named Jonathan as part of the Have You Been Paying Attention Quiz on Sunday.
It sees the pair asked about things which have happened during the week by a listener – with the first question of the segment being about Peaky Blinders.
And it led to a gaffe with the Black Country Living Museum in Dudley, the answer to the question, being labelled as in Birmingham despite the museum's obvious name.
Jonathan asked: "Peaky Blinders creator Steven Knight has said the story could potentially return to television with a new creative team. What museum is the series filmed in, in Birmingham?"
Matt said he "didn't know it was filmed inside a museum" which was backed up by fellow presenter Molly. The male presenter added the show was something he "tried to watch" but he never warmed to it – despite joking he was jealous of the suits and flat caps, but would look like a "little chimney sweep" if he replicated it.
Matt added: "It's got to be like a museum of old Britain, hasn't it? When is it set, like around the war isn't it? The museum of the 20s or 30s. Hang on, in Birmingham there's a chocolate factory. No, is there a museum of chocolate? No, they wouldn't film it there, that would make no sense."
The two presenters asked to be put out of their misery – with Jonathan revealing the answer, although he got the name wrong – saying "It's the Black Country Living History Museum" to which Matt responded: "of course, the BCLHM that one."
And the presenter added: "I think there are people who worked on Peaky Blinders who are going 'I don't know the answer to that question'.