Scale build up would be my first choice that is the start of a block heat exchanger symptoms, hot, cold then back to hot as the scale gets flushed out of the exchanger as pressure builds due to the blockage. Run the hot tap and watch the temp gauge, if it rises then falls its more than likely crud build up. At this stage it's pretty easy to fix, pop in some boiler clean and run the heating and drain after a couple of weeks. A good idea is to drain a rad each year if its got black bits in it then you protection is spent and the system needs a clean and protection recharge. If you have recently started to use your heating then crud hitting the exchanger is the first point of call.
If it doesn't clear the problem you can move on to mechanical boiler issues but at least you would have removed any blockage issues.
A diverter valve tends to get stuck and the heating won't come on or it comes on and sticks halfway and you get luke warm everything , rads and hot water or its stuck in the hw only and you get no heating. Or its stuck in heating position so you need to run the heating to get hw,
The other two components of the combi diverter are the pressure switch, which can get stuck wide open, look for scale around the pin that pops out to activate the switch, . but then would let the system run without pressure regardless or the membrane side which pin holes, but that would stop the boiler working pop the switch off and see if the pin moves in and out freely, it should with water and pressure in the system be easy to push in then should slowly spring out. The temperature sensor could be failing but again you would notices the boiler going to lock out.
Basically once you are past the wet side you need a engineer in...