The dial on the front controls the temperature the boiler raises the water to before it shuts off – essentially a high limit stat.
The towel radiator/airing cupboard radiator are heat sinks to allow the system to dump heat if all the valves are shut. It can be done this way or it can be done with a bypass valve.
The boiler will run until the high limit stat reaches temperature. Once it cools sufficiently it will run again.
A stat. will stop the boiler running once the location where it’s placed is up to temperature. It will probably be a bit more efficient as the heat sink rads will not be heated all the time but I would doubt massively so.
As northernmatt says, a stat is dead easy to fit but may require the boiler to be disassembled.
I’ve used altech stats from Graham’s the plumbers merchants which are cheaper than honeywell and work ok. Stats are a bit of a minefield as there’s wireless, wired, programmable etc.