There are two solenoid valves in the airing cupboard (not a 3 way).
Do you mean this type of valve?
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If so, they are motorized zone valves, not solenoid valves. One controls the flow through the radiator circuit, the other the flow through the hot water cylinder.
From your description, the heating valve is stuck open for some reason.
Disconnect the brown wire (this removes any power from the motor) and see what happens.
If the problem goes away, then power is getting to the motor when it shouldn't. This comes from the timer CH ON terminal via the wall thermostat.
If you still have the problem, there are two possibilities: the valve is stuck or the switch within the valve is permanently closed.
On most valves you can remove the actuator (box on top) to reveal the valve spindle. this should rotate easily, but only about 20deg from open to closed. If it is stiff, try a
small amount of 3-in-1 or WD40. If very bad, you will have to replace the complete valve.
If the spindle is free, the problem is with the switch in the actuator. The contacts sometimes "weld" together. You may be able to free them and clean with glasspaper. If not, you will have to buy a new actuator.