F expressed precisely :
In the fault state, the silver lever below the valve can be freely moved left
to right and back with no resistance. If I take the actuator head off the
valve the lever springs to the left to the closed position.

When the room stat is calling for heat I assume the valve is driven open and
held open but is it driven closed once the stat is satisfied or the hold
released and springs are left to close it?

Though the fault has rectified itself a couple or three times, am I right to
assume I'm looking for a new actuator head?

Often they use a spring return and the spring fails to close it because
the valve is stiff, or the actuator worn. In that design, the motor
continues to be powered, but on reduced power whilest ever it needs to
be open. If the actual valve is free, then replace the actuator - you
should be almost able to turn the D of the valve, with your finger tips
if it is free.

Another type is called a MOMO, where there is no spring return
involved, the motor runs to position then switches off, then moves to
the next position (as required) and switches off. This type only
rotates the valve in one direction, rather than back and forth of the
spring type.