it was a question of inviting manufacturers to make an offer, and BMW did. As for 'Made in Britain', BMW makes the Mini at Oxford. Rolls Royce cars is also part of the BMW group; you can't get more British than that, although I doubt that anybody will get driven to the venues in a complimentary Rolls.
Who will drive them? Presumably they'll be driven by people appointed to do the job by the Olympic organisers.