Hamleys

Hamleys founder, William Hamley opened his first toy shop in 1760, around the time of the earliest dissected puzzles, calling his store at that time Noah's Ark in London's High Holborn region. The flagship Regent Street branch was opened in 1881.Source:Wikipedia
Wooden jigsaw puzzles were certainly retailed through the stores from the early part of the twentieth century. These were cut and branded for the store by known manufacturers of the time, including Raphael Tuck, see Chrysanthemums, and William Peacock, see Fruit Blossom as examples.