Hello and welcome.

I'll ask a moderator to merge your posts.
You can modify your own post for an hour afterwards, and 4 images can be posted per post.
I've peered at the one booklet published on Art Cut glass - which unfortunately, dosen't have the best photography and it can be very hard to tell cut patterns from the images in it.
The one that most looks like yours can only be seen on a composite photo of a charger with a vase and two tumblers in front and i cannot see the patterns properly
It's nos. 44. 45 and 46, on p 14 of "Art Deco to Post Modernism: A Legacy of British Art Deco Glass" and was published to go with an exhibition curated by Nigel Benson and Jeanette Hayhurst and is written by Nigel. (He is not responsible for the photographs.)
Pic no 45 is a "Flower centre" vase, cut with stylised sunflowers (it can't be that, surely?) pat no 28339 late 1930's -50's and features in the 1952 catalogue.
It's a flared footed vase though, not a bucket like yours.
There's another flared footed vase, pic no 55, vase cut with vertical and horizontal panels and intaglio cut floral sprays, pat No. 28398 late 1940s -50's.
But there's nothing else there that looks like this.
Maybe somebody else who knows more about cut stuff than I do can help you more - it's not really my area.