Yes, in the main they fit on a base, two screws at bottom hold the programmer to base, you slack them off don't need to fully remove and old unit hinges off and new unit plugs in, always do with power off as there are live terminals you can touch, but no wiring as such.
However you say "Turned the thermostat right down but heating stayed on." which does not seem to point to the programmer.
So I suspect a motorised valve micro switch has stuck? Basic way central heating works, programmer sends power to thermostat, and thermostat sends power to motorised valve, and once valve is fully open it sends power to boiler.
The micro switch sticking is a reasonable common fault, however can't really change the micro switch, you have to either swap motorised valve head, or whole valve.
So I think you will find even with the programmer removed, boiler still runs?
So you could try gentle tapping the motorised valve and see if micro switch opens again.
Many thanks for a helpful reply. Before calling a plumber I'd like to try tapping the valve - I presume it is part of the collection of pipes and controls around the hot water cylinder in the airing cupboard. How do I recognise it?
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