Is china so powerful that in theory it could invade places like england and europe if it wanted?

I wouldn't worry about it, they're much better off trading with us than fighting and they know this. If China ever did decide to invade Europe they'd have quite a distance to come and USA, UK and France have plenty of nuclear weapons to go round. There is much more of a danger of war between China and its neighbours, there are some islands and resources that Vietnam and the Philippines think belong to them but the Chinese think is part of China.