Thanks for those replies.
Breesey - roughly how much is a new stat for the cylinder and is it a job that a novice could do?
Agile - do you mean turn off all the rads individually? At least then I would have HW while I get it sorted and not fry in the process!
I have an older looking conventional Potterton gas boiler in the house I've just moved into (not sure of model but can find out if needed) with a hot water cylinder and two motorised Honeywell valves. Tank thermostat set to 70F and boiler thermostat on 3 (out of 5).
CH works fine. Radiators...