Cue complaints from Activision, Ubisoft et. al. complaining that the BBC's core business is in broadcasting - not writing games - and that this will put them out of business.
Just the same reason there is no iPhone app to neatly retrieve the BBC news.
Private Dentists compete against NHS dentists, people still pay for private medical care rather than use the NHS. Private schools are doing well...
That said, I bet this game will be rubbish because the BBC budget won't be a patch on what was spent on, say, Modern Warfare 2.