Marris Antiques has dated this piece to the Georgian era.

Although it is probably that this is a family crest, it is possible that the engraving relates to a Unicorn Tavern of which there are a number in London from early as the mid 17th century. Possible associations include the Unicorn Tavern in Henrietta Street, Covent Garden (1774 - 1789 and 1801 - 1827). The Unicorn, Clare Market (c1760), the Unicorn in Suffolk Street, Charing Cross (1770), the Unicorn Tavern Hoxton Old Town (1809 - 1827) and the Unicorn next to the Grasshopper, Lombard Street (1794 - 1874).
Information from Antique Sealed Bottles 1640-1900: and the Families who Owned Them by David Burton and Christopher Mortimer Antique Collectors' Club volume 3, p. 1452.
Marris Antiques has dated this piece to the Georgian era.
Robert marris specialises in 18th, 19th and early 20th-century english and irish glass.
You can view the stock and full dealer information on the Marris Antiques Profile Page