The Russians were mentioned in the previous post.
The Australians retook Borneo and other islands in the Dutch East Indies during June and July of 1945 with U.S. naval support.
The British were finishing up their campaign in Burma in the summer of 1945, capturing Rangoon in early June. They were also actively planning “Operation Zipper,” the invasion of the Malay peninsula. In June, Lord Mountabatten set the date of invasion as September 9.
Then of course there is the famous Task Force 57 (when attached to the Fifth Fleet)/Task Force 37 (when attached to the Third Fleet). This was a multinational (almost entirely Commonwealth) force that included heavy representation from the RN that was active in 1945, including operations off the Japanese home islands during the summer, and would have participated in operations during the invasion of Japan.
The armoured flght decks of the British carriers proved their worth against kamikaze attacks off Okinawa and Japan.
According to Wikipedia, the last time a British battleship fired its guns in anger was when* King George V* bombarded the Japanese town of Hamamatsu.
This summary is not all inclusive, but at least should give a clear idea that the British and other allies were not waiting idly while the U.S. finished up the war alone.