radiators seems to be linked. Yet looking at my boiler with the cover
off shows two thick pipes going in on one side and two thick pipes going
in on the other. One pair of pipes gets hot and heads off to the hot

Yep. You appear to have gravity circulation. I would recommend upgrading
this. The simplest method would be to add a 2 port valve, pump and cylinder
thermostat. This will stop the water getting too hot, save energy and reduce
boiler cycling. In the longer term, the systems can be combined when you
replace the boiler with a single circuit controlled by the 2 zone valves.
You then only need one pump.

You also say there is no room stat. Add one ASAP (and a zone valve if it has
none) and make sure other rooms have TRVs too. You are wasting gas like it
grows on trees.

Christian.