The RN may have shrunk, but:
In the 17th - 19th centuries (and the early part of the 20th), the RN maintained dominance over the seas by two means. One was to have more ships -- British government policy at the time varied but was based on the principle of having a larger navy than the next two largest navies in the world combined.
The other was by having the best seafarers. Even in the days of press-ganging, the RN took its crews from the merchant marine and other seafaring communities where available, and spent time at sea training them. Typically, during the wars of Napoleon, the Spanish and French navies were recruited from the countryside or from the army.
The days of having the largest navy may have gone, but the days of having the best navy may have not.