It is called the “two-power standard”. The times of naval superiority at low cost was at an end by growing naval competition from old rivals, such as the French, and new ones such as Imperial Germany and the Japanese. These challenges were reflected by the Naval Defence act of 1889, which received the Royal Assent on May 31 1889, formally adopted the two-power standard and boosted British naval strength. The standard called for the British Royal Navy to maintain a number of battleships at least equal to the collective strength of the next 2 biggest navies on the planet, which then were the French and Russian navies.

Expert naval opinions displayed to the parliament in December 1888 and February 1889 provided critical views on the state of the navy. The buildup and expansion of the French and Russian navies was another factor pointing to alleged British weakness. As a result, public support for proposed naval growth grew and placed further pressure on Parliament to support the act.

In reality, the two-power standard had been informally utilized over the past 70 years and during the 1850s, Britain had briefly met it. Britain already enjoyed international naval superiority. The Act reasserted the standard by its formal adoption and indicated an ambition to bolster British naval supremacy to an even greater level.

The expansion came in the form of 10 battleships, 42 cruisers and 18 torpedo gunboats. The battleships were the centrepiece of the legislation. 8 first-class battleships of the Royal Sovereign class and 2 second class battleships, HMS Centurion and HMS Barfleur were ordered. The Royal Sovereign class was the most formidable capital ship of its day, fulfilling the role of a larger and faster battleship unrivalled by those of Russia and France. The cruisers were aimed at protecting the British supply lines.

9 first-class cruisers of the Edgar class, 29 second-class cruisers of the Apollo and Astraea classes and 4 third-class cruisers of the Pearl class were provided. The other 18 torpedo gunboats served to assist and defend the main battle fleet.

The major rationales were military and economic. The First Lord of the Admiralty, Lord George Hamilton, argued that the size and scope of the new building programme would deter and discourage the naval ambitions of other powers. By deterring other powers’ naval growth at present, the British would be able to spend less money on shipbuilding in the future.

I'm at work at the moment so I don't have my books to hand so hopefully this doesn't get removed.

I actually wrote my dissertation on this! Or at least the naval arms race prior to WW1 and the development of Dreadnought class warships.

Britain had the largest navy in the world and its policy was to ensure the Royal Navy was at least the size of the next two largest navies, known as the "2 Power Standard".

(Carl Cavanagh Hodge (2008). Encyclopedia of the Age of Imperialism, 1800-1914. Greenwood. p. 549. ISBN 9780313043413.)

Apologies, I'm posting from my phone so can't really reference properly.

I hope this helps!