When the heating is on I have hot water but if I turn the thermostat down and the heating goes off I have no hot water. This happens when the timer has shut down the heating also.
The pilot is on, there is sufficient pressure and the system is at the optimum level.
Not an expert but we've had a similar problem on at least 3 occasions. It's usually caused by the Diverter valve. The motor on top of the Diverter valve seizes or stops working. These are available from screwfix for about £10.
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Try fixfault.com to fix home heating systems.