Hmmm!
Bagley 1333 'Wyndham'
Not quite.
... so Bagley Wyndham it is ...
Ditto.
... in a former thread I was told British Made IS Bagley ...
Nearly.
It ... had the option of a black oval or self-coloured plinth
Not quite.
Perhaps I better explain — and I am bound to be accused of nitpicking.

Pamela — Bagley used
British Made, but sometimes other texts, like
Made in England. Other glassworks used
British Made, for example I am sure that I have seen it on a Wood Brothers piece, either an eyebath or a baby feeder, although they also used
Made in England.
Mod: Paragraph altered as requested by Bernard.Gill et al — What's it called?
It first appears to my knowledge in the
Pottery Gazette advertisement of September 1, 1934, thus, in the absence of earlier primary material, giving us a likely launch date. As it was the first of the two 1333 vase sets, it would probably have been known then as "Vase on plinth 1333".
The second, the diamond-shaped set, was apparently launched in the PG advertisement of April 1, 1936, and was described as "Vase on plinth 1333 D". I think it is reasonable to presume that it was then, Gill, that your pointed oval set became "Vase on plinth 1333 O", which I have seen handwritten with a solidus thus "1333/O".
The name
Wyndham was applied to the 1333 range post-war, so if your set, Gill, was then no longer in production, it is not strictly correct to call it
Wyndham.
Christine — Option?
Yes, these sets are found today with both matching and black plinths, but I know of no evidence that Bagley sales and marketing ever offered an option. Of course, if a major chain store or wholesale client had a particular preference, the Bagley salesman was hardly likely to object! Alternatively matching plinths could have been an exclusive for one major client. We just don't know, and there are other explanations / scenarios. Note that the 1934 advertisement shows a black plinth on the oval set, and the 1936 advertisement a matching plinth on the diamond-shaped set.
I hope that clarifies this set's history a little.
Now you can throw brickbats at me.
Bernard C.