Cheers! Yes, it's a nice set.
That type of handle is typical of the British razors from the end of the '40s through into the '50s. They are most often seen in the Deluxe sets, which are clamshell cased similar to the '30s Streamline sets but more rounded. Later still, the handles became lighter and were made of aluminium. Those lighter handled examples can also be found in the (late) Deluxe sets and the Peerless sets of the '50s.
This particular case was also seen the '30s. I often doubted this, but I finally got my proof with an Australian 150th Anniversary labelled set which bore the 1938 date. I believe the case is exactly the same but the razors were different. In the '30s they were the chain link handle for Ever Ready (and British Made GEM branded for Australia). I also have a Star in this type of case but cannot figure out the exact era ... I think it's '50s.
I would hazard a rough guide at the more mottled bakelite being earlier and the more plain (like this one) being the later date.
Nice, thank you sir!