Local licensing authority for Newmarket is West Suffolk
In 1869 Benjamin Chennell is listed as a brewer and importer of foreign wines & spirits at the White Hart brewery.
The 1874 White's Suffolk Trades Directory lists Benjamin Chennell as a brewer & wines & spirit merchant and victullar of White Hart commercial hotel.
In 1896 Benjamin Chennell's White Hart brewery and Charles F Moody (Kings Head brewery) were acquired and registered as Newmarket Breweries & White Hart hotel Co Ltd.
Nearly acquired by Greene King & Sons Ltd in 1896 but subsequently sold to Star brewery (Cambridge).
A brewery is shown behind the White Hart on the 1901 OS map. Presumably it's this one?