Of course Jaques cannot be missed, as they started the “Staunton” model. See English makers Jaques.
Another well known manufacturer is Ayres. See English makers Ayres.
A somewhat mysterious company is B&Co. See English makers B&Co.
And see others English makers Others.
20th century makers Mildred Rose and Britain made lead sets based on the “Staunton” design. You find them on “The Rose Chess” and Britain pages.
On the Plastic page more “Staunton” sets of manufacturers like Grays of Cambridge and House Martin. And some unknown others.