According to Wikipedia, the RN had the following in 1877:
"The total strength of the British navy in 1877 was 533 vessels, of 677,883 tons, and which carried 5080 guns, some being of the enormous weight of 81 tons. It should be explained, however, that more than half of these were returned as ?in reserve and building?, the number in commission being 230 ships, with a tonnage of 307,072 tons and 1939 guns. The ironclad fleet comprised 61 vessels, many of which were of far more powerful construction than those of any other nation in the world. ? There served in the fleet in commission 25,500 officers and men, 2854 boys, and 6385 marines, being a total naval complement of 34,770."
This was essentially the most powerful navy in the world at that time, and was also close to industrialised sea warfare.
According to the RN website:
The fleet greatly increased in size, from about 270 ships in 1700 to about 500 in 1793 and almost 950 vessels in 1805. The larger size fleet required more seamen. In peacetime the numbers were much less than in today's Navy and varied from 12,000 to 20,000 men during the Eighteenth Century.
Numbers like this are unlikely unless you are facing a major naval foe, with extensive travel across the world required. However, with less technologically advanced ships, greater numbers are possible. Venice in 1450 had over 3,000 ships in operation, most of which could be converted to warships as needed.