The 45-year-old winner of Celebrity Big Brother 2010 was sentenced to eight weeks in prison after being convicted of contempt of court for giving a false statement in his insurance claim.
Reid attempted to claim compensation after his Audi A6 was involved in a car crash with a Seat Leon on the A41 in north London in 2018.
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The former cage fighter said a stranger on a motorbike had volunteered himself as a witness before police arrived on the scene.
But the witness turned out to be kick-boxing champion Darren Summers who trained Reid for his first cage fight.