Update.
I got another contact pin from BMW (part number 12 52 1 427 612 - about 70p), spent a hot afternoon digging the old pin out and crimping a new length of wire, and hey presto, fan works.
Before you all say "we told you so", I've had two renowned BMW independent garages fail to sort this, at my expense. I'm going to go back to Walkers and argue their incorrect diagnosis and see what they say.
Fixing this was one challenge, getting anything out of a garage will be another.
I now have a spare fan (along with radiator and condenser) if anyone is interested. Oh, that fan definitely works too!