Chris Langham, 74, who had a main role in the comedic television show, was convicted in 2007 of 15 counts of downloading and possessing child pornography, according to the Telegraph.
Langham was banned from working with children for ten years and was forced to register as a sex offender due to court orders, according to the paper.
The actor was arrested during Operation Ore, which was an investigation into customers paying with a credit card to access child pornography on the internet.
Langham, who recieved the 2006 Bafta Best Comedy Performance award for his role as Hugh Abbot in "The Thick of It," was sentenced to ten months in jail, but had it reduced to six months on appeal, the outlet reports.
The National Association for People Abused in Childhood (NAPAC) denouned the BBC's decision to air episodes of the show and urged those who could possibly be "triggered" by the re-runs to call its free support hotline.
"We know there’s an impact from watching certain things that can retraumatise people," an individual that works with abuse victims told the Telegraph.
The show's writer and creator, Armando Iannucci, first made the announcement that the BBC decided to air episodes of his award-winning show on Twitter writing, "Oh, by the way, every episode of The Thick Of It now back up on BBC iPlayer."