It looks like I'm going to have to pay for a new one but they are not cheap.
In the meantime I am frozen.
I think the bit wired into the boiler is a Honeywell BDR91. If I press the on (override?) button it turns heating on then soon turns it off. I think this is because the remote control unit is switched to 5 degrees so it heats to 5 then turns off.
That's what I get from Google anyway. Any DIY experts or electricians know any cheats to override this?
I'll keep searching.