John wrote:

I would think that the hallway would be a
better location for the stat but that rad has a TRV fitted. Am I alright
in just opening this TRV and telling everyone in the house that it must
remain permanently and fully open?

Yes.

I know it's a "bodge" and really, if I
want to move the stat I should drain the system, take the TRV off the
hallway rad, and install it on the living room rad, but that's such a lot
of messing and I'd rather wait until the system has to be drained for
whatever reason and do it all then.

It's not a bodge. What happens in a few months time if you decide that the
wireless stat would have been better in a different room instead of the
hallway? Just leave the TRV fully open, it'll be fine. If you're concerned
that somebody might turn it down then just remove the head from the top of
the TRV.

OTOH getting an extra TRV and fitting it to the living room radiator might
be worth doing when you get the chance.

--
Mike Clarke