The two episodes were recorded back-to-back at the BBC's Edinburgh Fringe venue, for broadcast on Radio 4 later in August as part of the show's 85th series.
Before the recording started, a Radio 4 producer addressed the audience in the BBC tent, saying: "We apologise, Nicholas is ill tonight. I'm sorry we hate to disappoint but Gyles Brandreth will bravely cover both of tonight's recordings."
A source told the paper: "It's nothing serious. He's just got a bad back."
The Daily Mail reports that Brandreth joked to the audience "Nicholas can't be here tonight as he's auditioning for Naked Attraction on Channel 4".
This is only the second times the host has missed episodes. Last June he missed a recording due to flu, with Brandreth also hosting those episodes.
The actor and presenter is also hosting his comic chat show Nicholas Parsons' Happy Hour at the Edinburgh Festival, with dates booked for the 8th to 11th, but it is currently unclear whether these shows will now go ahead.
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