This is the thermostatic valve from a shower:

https://www.dropbox.com/s/16k3277d94...valve.jpg?dl=0

The mixer I removed it from has no markings, and this valve barely has
any - just some numbers on the brass spindle at the left.

When the unit warms up, the section on the left moves outwards, opening
the gap you can see to the right of the first black rubber seal. This
allows more cold water to flow in through that gap, and out into the
mixer.

The problem is that the mixed water never gets hot enough, so either the
thermostat mechanism itself is too cautious about hot water, or the
valve is unable to restrict the entry of cold water properly (I suspect
this).

I think it's probably unlikely I will find a replacement for this, and
instead will need to replace the whole mixer. Before I do, any
suggestions for identifying it in order to find a replacement?

Thanks,

Daniele