If it is the same as the one I had PeCo, it is indeed a Villiers engine. I don't know about the 150 cc, mine had a rather small bore and very little power. Rather a sweet little engine, easy to start, but it used up two magnetos (coil breakdown) and the lack of power was annoying.
I put new rings in mine just by buying a set from the nearest mower shop, but that was years ago. They may not stock them by now. I broke the impact starter spring relatively recently (about 5 years ago) and bought a second hand one from a mower wrecker. Unfortunately the second magneto gave out about a year later and I scrapped the mower, with a sigh of relief.
If you can't get rings any other way, you could try a mower wrecker. Some of them have quite a lot of knowledge of which engines can, by sheer luck, be serviced by parts made for other engines.