Found new owner
H. Simmons was one of the most famous London tobacconists with a long history and very nice tobacco shop in the Burlington Arcade. The pipes were ordered from different sources including the Dunhill company. In the 1980 the business was acquired by Dunhill. We can't confirm that this pipe was made by Dunhill; but it's anyway a wonderful piece of briar and great addition to any collection.
The pipe markings are "H. SIMMONS \ BURLINGTON ARCADE", "MADE IN LONDON \ ENGLAND", "G602". The length is 16.0 cm (6.3"), bowl's height is 5.0 cm (1.97"). External diameter of the bowl is 4.2 cm (1.65"), internal diameter is 2.0 cm (0.79"). The depth is 4.0 cm (1.57") and this pipe weights 58 gr. Briar, vulcanite stem, no filter. The chamber has been protected with a break-in coat.