If you turn the sound on, you'll hear Smith quoting Patrick O'Flynn, the UKIP MEP and former communications chief, warning that the party risks turning into "an absolutist monarchy and personality cult". Although that's not quite what he ended up saying.
Luckily, Smith made a smooth recovery and continued as if nothing had happened.
People on the internet were, of course, very amused.
Mind you, it's still not quite as funny as this James Naughtie slip-up on the Today programme.
Robert Colvile is UK News Director at BuzzFeed and is based in London.
Contact Robert Colvile at email@example.com.
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