I am a UK citizen going on RTW trip starting in January. As part of my trip I am going to China in June. However, I am confused on how I am going to get a visa? It appears that I won't be able to get it in January as it will have run out before I get to China! Any advice?

Before going to China I will be in Tokyo for 3days, and LA for 3days before that so I was thinking I could try and get a visa there, but may not have enough time and can I get a visa for a British citizen in these countries! Hope you can help me.