discover I need TRV on ALL the rads rather tham all but one, and
a room stat into the bargain.

You are mistaken. Fitting TRVs on the room with the room stat is not
permitted by regulations and will make energy consumption worse, as it
defeats the boiler interlock.

If you wish to have all rads with TRVs, then you'll need to abandon the room
stat and fit a flow switch interlock and possibly rewire the pump.

here's the part P question. how can I run the connecting wire for the room
stat from the boiler to the living room ?

Use an RF thermostat. No fixed wiring required. No redecorating. As the
central heating is on the other side of an FCU, you can probably get away
without Part P.

You can get cheaper ones than the following, but it is the best. (Honeywell
CM67RF).

http://www.plumbworld.co.uk/761-12687

Christian.