I think when Sludge referred to Bailey as a regular commentator and pundit for the right wing on BBC radio 5 live phone in, he obviously didn't mean he was a presenter. Rather a person who built up his political profile by often appearing on political talk in shows representing Conservative/right wing views whilst others would similarly have opinion from the left, centre, nationalist etc.
Don't let your misunderstanding stand in the way of your rant about the perceived political bias of BBC radio presenters though.