A little background on ordering BMW's in the USA. If the dealer has ordered a car for speculation, i.e, not ordered under contract for a customer, any time up to maybe as late as a few days before scheduled to be built, if he sells one, that one in the production line can be changed to reflect the customer's wishes. If the dealer does not have any 'committed' vehicles in that queue, and must enter a new order rather than changing an existing one, he has to wait until his allotment allows more. Depending on the car involved and the current market, that may entail a wait of a month or maybe even more before it can even be ordered. What usually happens, though, is the dealer will try to find a vehicle in inventory somewhere nearby and swap or buy it from that dealer to fulfill his sale. When I bought my i3, the dealer found one meeting my desires and had it trucked up, and I had it in about a week verses maybe months of waiting for it to be built.
The UK market is likely different, since corporate buys the cars, but their shipping time is less than to the states which helps.