I have a feeling that either Willis didn't patent these things, or if they did, then it's now expired, as there seems to be several different manufacturers of them. This probably explains why there are now several different types of essentially the same thing. Once upon a time, the only manufacturer was Willis Heating, in Belfast (https://willis-heating.com/ ), but it seems that Willis have expanded into lots of related areas and don't seem to make the Willis heaters any more.
I first came across them nearly 30 years ago, as they were pretty commonplace in parts of SW Scotland, as well as NI (probably because it was often quicker to get stuff from Belfast than it was from Ayr or Dumfries, at least for those out where we used to live). Not often fitted to new builds, but they seemed a pretty common fit to houses that had things like back burners providing hot water. The second house we bought when living there had a Baxi stove for hot water, with a Willis heater fitted alongside the cylinder. Seemed to work very well, really handy for heating a bit of hot water very quickly if the stove was out.
You can now get versions with a 1 kW immersion, and I have wondered whether one of those, fitted with a thermostat set for around 45°C and plumbed in to the hot feed under the basin might not make for a handy way to get instant hot water for hand washing. They hold around 4 litres, more than enough for a quick hand wash.
Found this close up of the labels on a Willis (actually an Emerald Geyser version) that shows clearly the direction of flow and has a sensible warning that the whole thing has to be filled with water: