I used to own all three sets, in fairly minty condition too. Sold all three as a set for $150 a number of years ago.
Wish I still had them. They would be worth about a grand today.
Edit: added pictures of them.
If there's no number on top of the baseplate then it's a '20's thick cap OLD type. It looks like it's a gold plated razor, although some of the plating may be worn away. The English sets are sometimes unique to England and won't have an identical counterpart in the US sets. I've never seen a set identical to yours, but it's a nice set, and a fantastic shaver. I have several '20's OLD types and they are some of my favorite razors.
Thanks mate
Hi yes there is a small cracking along the handle . Spoils it a little but could be glued back.If it was the razor alone for £25 then it would have been a touch on the high side but with the case in such good condition and the blade banks that's an excellent price IMO.
The ball-end isn't supposed to pop out like that but it's very common for that to happen due to the press fit giving way over the years. If you look very closely you may see a tiny hairline crack in the end of the handle. If it bothers you it can be quite easily fitted back in and stuck in place - most guides say epoxy but I've used a good quality superglue on one of mine and it's been perfect ever since.
Not something to worry about though - It's pretty much the norm for a lot of the Old-Types and it really is the set that's the star there.