Between Hyde Park and Kensington Palace, Kensington Gardens have often been considered an extension of Hyde Park. It was originally part of the park until it was separated by Queen Caroline in 1728. The creation of the Serpentine, between 1726 and 1731, helped accentuate the boundaries between Hyde Park and Kensington Gardens.
The Royal Parks website has a wonderful interactive map of the park: https://www.royalparks.org.uk/parks/kensington-gardens/map-of-kensington-gardens
By all accounts, Kensington Gardens during the Regency era were a fashionable, popular place to promenade. According to Regency descriptions, it had been a long standing favorite for walks or carriage rides for at least a hundred years.