I’d look at the motorized valve for the central heating if you say you’re getting hot water on demand, but no heating.
The motors inside the valves eventually burn out as they are designed to jam when the valve is open. The motor drives against a spring which will automatically close the valve when the motor is de-energized. Not a very sophisticated solution, but it works! These motors cost about £7-10 and are easily changed if you have a bit of heatshrink sleeving, solder and an iron.
There are different ways central heating is configured and wired up and the set up I have is called an “S-Plan”. With a combi, circulators and valves are often built into the boiler casing. Your boiler manual and Google will enlighten you as to what you have got. If you haven’t got the manual, see if you can get it from the manufacturer’s website.
What happens in many systems is the programmer switches on the hot circuit and all this does is energize the motor in the valve.
When the valve is open, a micro switch inside the valve casing is made, closing a circuit that runs back to the controller circuit board in the boiler. This in turn starts the circulator (central heating pump) and it also “calls” the boiler into action. Soon after your rads should get warm.
If you locate the valve body, there will be a small overide lever which you can actuate. The lever may be a little stiff, but when drawn across to the open position, this should enable the central heating to kick in. It will stay on permanently until you release it, thus rendering the programmer redundant.
So that’s where i’d start. Good luck and let us know what the actual problem is/was.