Why did Britain agree to attend the Washington Naval Conference?
There was a great deal of anti-war, pacifist sentiment in Europe after World War I. It had been such a horrible catastrophe, that no one wanted to repeat it again. Thus the desire to attend arms control meetings like the Washington Naval Conference, or to sign on to non-aggression treaties like the Kellogg-Briand Pact.
A second reason for Britain's willingness to go to this meeting was that they had the upper hand on the high seas with the Royal Navy, so if the agreement forced other countries to limit their navies, then Britain would guarantee its long term dominance. The final agreement allowed Britain and the US five "capital" ships (such as battleships) for every three owned by the French and Japanese, and every one owned by the Italians. So they came out on top at the end of the agreement, and the US focused its navy in the Pacific.
I am sure that your book has a specific answer that you are supposed to come up with. This is the kind of question that can have different answers based on the opinion of the scholar who is writing the book.
Most historians believe that the British agreed to attend the Washington Naval Conference because they were economically weak after WWI. The war had cost a lot of money and they could not afford to build the kind of ships that they would have needed to build to maintain their superiority.
Because of this, they attended the conference in hopes of getting eveyone to limit the size of their navies. This would make it so Britain itself would not have to build a huge navy that it could not really afford.