No, you should be able to have hot water and heating at the same time. Assuming that both the room and cylinder thermostats are calling for heat of course.
Anything been changed recently?
Is there a manual regulating valve in the hot water circuit to the cylinder? has it been closed down too much, so that the resistance is too high preventing the water circulating when the radiators are on as it offers a lower resistance?
If you have a manual by-pass, has it been opened too much, so that there is insufficient flow left for the hot water and radiators at the same time?
Is the pump set at the correct speed for the size of the system?
If the system used to work correctly and nothing has changed, you can check the motorised valve by observing how it operates. If you are able to safely take the top off and see what happens to the mechanism, you can check its operation as follows.
1. Make sure that both the cylinder & room thermostats are calling for heat (on)
2. Switch on the hot water only at the programmer. The valve mechanism should sit at one side fully pulled across by the spring. (hot water only position)
3. Leave the hot water on, and get someone to switch the central heating on at the programmer, whilst you watch the valve. it should slowly start to wind its self across, but not fully. You should hear from one of the microswitches inside click. The valve should now be in the mid position. (hot water & heating)
4. Whilst the heating is still on, switch the hot water off, the valve should continue to travel in the same direction as before, and after a click from the second microswitch stop at the opposite side from where it started. (heating only)
5. With the heating still on, switch on the hot water and check the valve returns to the mid position
6. Finally switch off the heating, leaving the hot water on, and the valve should be pulled by the spring back to its original rest position