The confusion as to whether "Whose Line is it Anyway" (WLiiA) is originally
BBC or
Channel 4 is because it was originally a comedy show on BBC
Radio 4 in 1987. After a year it then moved to television but on Channel 4.
WLiiA was originally a two teams improvisation panel show which was basically an attempt to update the format of the venerable BBC Radio comedy "I'm Sorry I haven't a Clue" (The home of Mornington Crescent). In fact the pianist on the radio version of WLiiA was Colin Sell who is also the pianist for "I'm Sorry I haven't a Clue". Richard Vranch took over as the musician for TV. The chairman was always Clive Anderson though on radio the regular team captains were John Sessions and Stephen Fry.
I would guess the show was either going to be cancelled or wanted to transfer to TV and Light Entertainment weren't interested (This happened several time with BBC radio comedies). It ended up going to Channel 4. After the transfer it evolved into the more open (non-team) game we know and love.
While I consider him to be good comic actor I think the radio version of WLiiA proved that Stephen Fry should neither be allowed to sing nor attempt to improvise song lyrics (no concept of metre or rhyme).