Thanks all for the suggestions.
After taking the glass off and metering the terminals, all the right voltages appeared in the right places. I then removed the central Torx screw that securing the actuator to the mirror body and discovered one of the connector pins was bend backwards. Clearly someone had previously forced the plug in, bent the pin and not bothered to test it. Bent it all back straight and all works perfectly now!
Also of note was that the lugs that held the back of the actuator on were all broken off, and the two white plastic guides on the back of the glass are missing. Amongst the pile of invoices that came with the service history was one from a Volvo dealer for replacing a wing mirror. I do hope it wasn't they that left it in such a mess
.
Anyway, all's well that ends well. No cost to me, working mirror.