Any idea to this part?

The dealer calls it "Bren Mk. I Tripod Grip" but I never saw it:
Attachment 128750

It is for holding the butt handle and normally attached to the strut of the tripod.
Originals are quite rare but a reproduction run was made several years ago in the UK.
You might find two small holes in the tripod strut for the rivets where it attaches