The Royal Navy was a naval division of the armed forces of the United Kingdom, a nation on Earth.
The first ship to bear the name Enterprise, the HMS Enterprize was a captured French ship and reflagged for service in the Royal Navy. The Royal Navy fought in the Battle of Trafalgar against the French and Spanish under the command of Lord Nelson aboard the famous HMS Victory. One participant in this famous naval engagement was an ancestor of Jean-Luc Picard, captain of the USS Enterprise-D.(Star Trek Generations)
The Royal Navy continued to exist into the 22nd century. Malcolm Reed's family came from a Naval background – the Reed men had been Navy men for generations, including Malcolm's grandfather, who served as an ordnance officer. As a child Malcolm wished to serve in the Royal Navy but later found he had fear of water – this was a great disappointment to his father. (ENT: "Silent Enemy")
The Royal Navy may also have controlled at least two spacefaring ships in this period, the HMS New Zealand and the HMS Lord Nelson.