To try to work out why the valve was rattling, I gave AP Racing a call.
They were helpful. and I ended up speaking to one of their people who knew about TVRs.
The valve shouldn’t rattle. They are happy to take a look at it (but that isn’t so easy for me).
It would be worth running the same pads front and rear. They supply TVR Power with AP Racing DS25HP pads.
It is possible that the front pads are somewhat aged, so fitting new pads and beddign them in might fix the problem.