I think you will have to obtain an independent engineers report to take this forward. They would have report that BMW had been negligent with the work they carried out.
Suggest that if you are a member of the AA/RAC that you phone their helpline for advice.
Without such a report, it is difficult to say whether the BMW garage were at fault or not.
It might be cheaper and less hassle, to get the car towed to a decent independent garage, who may carry out the repair at much lesser cost. The danger is that anyone carrying out the repairs might find more work that needs to be carried out. I am not sure I would want a BMW garage to start finding extra work, given the amounts they charge.