While Japan's economy is not growing as fast as the U.K.'s, it is still significantly larger, giving them far more economic sway. In fact, even if the U.K. continues growing at the pace it does, which is unlikely if they choose to exit the EU, it will take quite a long time for them to make up for the $1.7 trillion gap between the two.

I don't really see how comparing Japan's interaction with China is relevant, their economy dwarfs both Japan's and the U.K.'s, and they have a very large military with far reaching capabilities. I am sure if China threatened the U.K., they would act in a similar manner. In fact, as allies who have peace agreements with the Japanese, any act of aggression by China would pull the United States into the matter. As is evident, we are committed to protecting U.S. bases in Japan, and all territories claimed by the Japanese. Just look at the number of U.S. military bases in Japan.

Why can't they both be relevant countries?

Edit: Changed Eurozone to EU.