First, a note on British Music Publishers, Printers & Engravers By Frank Kidson, published 1900
Although the most famous publisher of British dances and dance music was John Playford and his descendants, there were many notable publishers throughout the 17th, 18th and 19th centuries. In 1900, Kidson published a very thorough directory of all the ones uncovered by him in his researches.
There is a facsimile PDF at Petrucci
There is a complete searchable HTML transcription on CGP's website.
Frank Kidson accepted that the listings in his 1900 work were not comprehensive and that his work did not involve an exhaustive combing of the British Museum holdings where many of the surviving published volumes were and are still lodged. His work is a starting point and further lists will ultimately contain more information that has come to light during the intervening century.
The following list draws heavily on his research.