Gertrude Antiques has dated this piece to the 19th Century.
Gilt lettering in good condition; similarly gilding on the base and handle. Some wear to the rim suggesting the mug has been used rather than kept as an ornament.

There is a Benjamin A Brickwell born in 1815 living on Church Street, Amersham, shown in the 1861 census. He qualified as an apothecary in London in 1841 and was a member of the Physicians Society of Guy’s Hospital.
No cracks or restoration, just the odd tiny black factory fleck.
Gertrude Antiques has dated this piece to the 19th Century.
You can view the stock and full dealer information on the Gertrude Antiques Profile Page