Just to complete the story on this issue:
Today Hazzy Dayz fitted the cruise control at my home address. Fitting was delayed due to bad weather before Xmas.
The result works perfectly - all genuine parts - and was fitted by their mobile Technician in one hour. Total cost for home fitting £314 - and despite claims that Audi dealers would match the price, I did not find one which came anywhere near.
Hazzy Dayz are based somewhere around Luton, but the Technician had just been to Cardiff Audi. Apparently they are specialists in some of the tricky electrical jobs Audi dealers don't feel able to manage themselves! Seems like a pretty competent company to me.