After serious thinking Jon wrote :
Should my radiators come on when the hot water comes on - even though
the heating is set to "off" on the programmer, and it's so hot in the
house that turning the stat up to maximum (30) does not cause it to
"click" on?

No it should not. You have a wiring error or a fault with the valve.
Call the installer back if it is a new system.

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Regards,
Harry (M1BYT) (L)
http://www.ukradioamateur.co.uk