Well, to answer my own question, the official BMW spare wheel kit for F10 to F13 cars includes a 135/90 17 inch light alloy wheel. The part number is 36112159862 and the price is between £380 and £450.
Having poked around on ebay, this seems to be quite a rare BMW spacesaver wheel size, last used on the E83 (X3) of 2003 to 2010 vintage. They are available from breakers. I just found one up for £130 and offered £70 delivered which was just accepted. Not to carry around in the boot, but to keep in the garage just in case I get a flat close to home. I just hope the 5 stud spacing and centre hole are the same.
This is what is going in the boot
http://www.ebay.co.uk/itm/Emergency-...4AAOSw-7RVDaXY
MPSS tyres are due for delivery late this afternoon. I'll report back when I have them fitted