A very solid explanation - Thank you - The boiler has one flow pipe but two returns - The hot water cylinder has a dedicated return pipe straight to the boiler - I am 100% sure of thatI think your system is quite unusual and it might be difficult to know what to search for.
The following bit is nothing to do with it being a one-pipe system. It is just an explanation of "gravity" and "fully pumped" systems
In the old days, two separate flow pipes would come out of the boiler. One flow pipe was pumped through all the radiators, before eventually returning to the boiler, in the central heating return pipe. The other flow pipe went up to heat the cylinder, but it wasn't pumped. The hot water would rise up to the cylinder by convection and then, when it had cooled after passing through the cylinder, it would fall back down to the boiler in the hot water return pipe. So, this setup was called a "gravity" system. And there were four pipes in total at the boiler, two flows and two returns.
Then in the 1980s, I think, we moved to a different set up. Only one flow pipe would come out of the boiler. It would pass through a pump and then would immediately be split by a zone valve (or valves) into two circuits. One circuit would be pumped to the radiators as before. The other circuit would be pumped through the cylinder. So that system is called "fully pumped" because both heating and hot water circuits are pumped. There is just one flow and one return pipe at the boiler.
Your system is different. Only one flow pipe comes out of the boiler and then, halfway around the main circuit, it tees off on a loop which passes through the cylinder before rejoining the main circuit. The cylinder effectively seems to being treated as if it was another radiator. I have no idea how common your type of system used to be. I know you are wondering why the water is not being "pumped" through the cylinder and that is tricky I think to understand and explain. I think the answer is that the cylinder loop is rejoining the exact same pipe very close to where it left it. So, there is no pressure difference between where it tees off and where it rejoins so there is nothing to force the water through the cylinder.
There is one shared flow pipe and one return for hot water and one return for radiators
Does that change anything about bending pipe or additional pump suggestion?