The 2001 Live and Kicking set was used for the BBC Scotland opt-out for Children in Need later that year. The L&K logo replaced with CIN. There's an image somewhere.
Not exactly the same but the set for Kate & Douglas's office in BBC's 'Kiss Me Kate' was used as someone's house in ITV's 'Barbara' - of course they both came from Carlton in Nottingham so it makes sense.
In the BBC1 broadcast of the Little Britain Series 2 sketch where Daffyfh goes to police station for a job as the gay community officer, The police reception set was used again as a police reception desk in a My Hero episode (in series 5)
Watch some of the old US sitcoms from the 60's re-using the same sets across the different shows was common as anything.
Speaking of Little Britain, the sofas and coffee table used in Boxing Day's Little Britain Night on BBC Three looked remarkably like an ITV regional news set.
I seem to remember Broken News or Dead Ringers having an extremely good mock-up of an ITV news set, so it was probably that.