Alan - You are still within your legal rights to reject this car as unfit for it's purpose, under the 'sale of goods act 1979' on all Three points of the qualifying criteria. 1) Not of satisfactory quality. 2) Not as described (as it does not work properly). 3) Not fit for it's purpose.
Read the Two articles below, both are from respected sources.. for more information.
http://www.autotrader.co.uk/advice/2010/09/buying/returning-a-car
http://www.adviceguide.org.uk/index/your_world/consumer_affairs/buying_second_hand_vehicles.htm
After having obviously tried the reasonable and friendly amicable route, it looks like you may seriously have to consider the legal option of redress for a refund, by contacting your Solicitor to ensure that you have, or are, correctly following the necessary legal steps required in the correct manner i.e. by first rejecting the car in written letter, then allowing for the garage time to respond in the appropriate manner. If you win your case which based on your post you certainly should, then the dealers will have all the legal costs awarded against them...including your lost earnings if you attend (do ask).
I would also advise you to contact this Solicitor before the car goes into the BMW dealers on Friday, to see what their opinion is on whether their involvement may possibly or prejudicially disadvantage your case or not.... should the garage you bought it from try to blame... or make claim that the BMW dealers have caused or made the alleged fault worse.
I presume this car will have been quite expensive therefore it will not be the small claims if under 5k, if over it will be the county court. I would make the pre-emptive legal strike that gives them either the opportunity to refund your money in full, or if they still refuse to act reasonably and within what the law states, then it's only themselves who will be to blame when they become burdened with all the legal costs on top, once or if, you should find it necessary to instruct Solicitors to initiate legal action dependent upon the final reaction from the dealers.