First thought is that a zone valve has stopped working.
This is a 3 port valve:
There are also 2 port valves that just have a straight brass part underneath the top box, unlike the brass 'T' shown in this picture.
There are a few different ways these can be set up, there is C plan, Y plan etc. You probably won't be able to determine what plan you have, but the common factor is zone valves and it sounds like that's your issue to me.
You can test them, there is a manual override lever on them.
If you can find a zone valve that has a pipe leading to a low entry point on your hot water cylinder, feel the pipe when your system is set to hot water, then operate the manual lever and see if the pipe gets instantly hotter.
If so then your valve has gone, usually not a massive job for a plumber to replace the valve.
There's also a possibility of a blockage in the pipework that goes to and from the cylinder heating coil, but the valve is the first thing I'd check.