Final posting on this:
Turned up at the Berne British Consulate 8.30 and had my cream-coloured Emergency Passport by 9:50 and on the train back to Geneva 10:30. So all that went smoothly.
Four other people turned up at the Consulate - all of them with passports stolen on the last section of the train journey into GVA on Friday or Saturday.
If you consider that there must be other people who don't lose passports but do have things stolen, then clearly there's a real problem with gangs targeting homeward-bound tourists travelling into Geneva Airport Fridays and Saturdays.