Quite a few on here with modern Mini's it seems so thought the following worth mentioning:
Tayna and Battery Megastore (to name but two) both use the same third party cross reference from UK registration to replacement battery. They both correctly identify model, date of manufacture, engine type and model reference in this case F54 series which equates to 2 litre B47 BMW diesel in Cooper D. Unfortunately they both take you to a range of batteries of differing makes but all of the 096 series, for this model type and maybe others.
These are all AGM suitable for stop/start with correct terminals BUT shorter, 278mm, and only 70 amp hour capacity, when they should be 315mm and 80 amp hour. Given the single fixed battery clamp location they cannot be secured even if one were to accept the lower capacity!
Needless to say the correct ones are considerably more expensive

Apologies but haven't found a generic code for this type. Nothing I can find on OE either.