The Major Players at the Washington Naval Conference of 1921
The United States, United Kingdom, France, Italy, and Japan were the major naval powers that negotiated the Washington Naval Treaty. They were all members of the Allied powers which defeated the German led Central Powers in the Great War, and they were all major colonial and naval powers that maintained significant battle fleets.
The United Kingdom's Royal Navy had long been supreme at sea, and had held it vital to maintain a fleet capable of taking on the next two largest naval powers simultaneously. As its colonial possessions stretched around the globe, it had to face the possibility of going to war with a European power like France or Italy aligned with Japan or even United States. Because of this, the Royal Navy maintained by far the world's largest fleet - dozens of battleships and hundreds of smaller vessels. But all this came at a cost - primarily that other nations were driven to match that portion of Britain's capabilities deployed near to them.
A successful Washington Naval Treaty would have to address this balance of power problem, and so the Royal Navy would inevitably suffer from any agreement. But, in return, the fleets of the other signatories would be restricted in size, reducing the number of ships Britain would need to maintain - a mutually beneficial result for all signatories and one judged to reduce the probability of conflict.
The synergistic nature of arms control caused it to be in each power's interest to come to a limitation agreement. Italy needed to be able to be powerful in the Mediterranean, France had to be able to guard its home waters in the Mediterranean and Atlantic, Japan was intent on being dominant in the Western Pacific, and the United States maintained Atlantic and Pacific Fleets.