Not strictly true. I spoke to BMH earlier today about the theory on this, without naming names, and the license agreement they have is that BMH are no allowed to build and sell new cars, as part of that agreement.
As I said earlier in regard to the rest of the trademark legalities, BMW own almost every right there is to the Mini in regard to shape and silhouette, how this affects the selling of new cars I couldn't say.
Whether it is part of the license bought by BMH or not, BMW will get revenue from a new build. However, I think it will be up to BMW's lawyers as to whether they wish to allow anybody else to register a new veehickle built with their parts. I suspect they won't.