I reckon it's more likely S-plan if the cylinder is unvented as there will already be a 2-port valve supplied with the cylinder (It is one of the safety features — if the water gets too hot, the valve is disconnected so that it closes). There are likely to be two or more two-port motorised valves in the vicinity of the cylinder. Follow the pipework — it should be pretty clear which one is for the hot water. (While it
may be Y-plan (with a three-port valve), this 2-port valve must always be fitted nonetheless).
Assuming S-plan:
I think that the most likely fault is the microswitch in the motorised valve head. When the system is calling for hot water, power is applied to this valve so that it opens. Once it is fully open, the switch is actuated and this switches on the boiler. A faulty switch will mean that the valve opens but it will not tell the boiler to fire up. If the heating is also on, the boiler will be on for the radiators and, since the valve for the hot water is open, will also heat the water.
It is possibly a stiff valve. If the valve is seized, it may not open enough to operate the microswitch. If you take the head off, you should be able to turn the spindle on the valve body easily with pliers, if not with fingers.
You can replace just the valve head without draining down or getting wet.
Motors do fail, and they are easily replaced. Every brand that I have seen uses the same type of motor (get a genuine synchron one),
https://www.screwfix.com/p/drayton-synchronous-motor/28670. However, if the motor was faulty, the water would not get hot at all.
I tried to replace a microswitch once but found that there are minor (but significant) dimensional differences between different manufacturers.
Julian F. G. W.