The great thing about London is that it has diversity without segregation. So no, you won’t find a huge area of town where almost everyone is of the same ethnicity, but the diversity is still there. Race isn’t the only index. A higher percentage of London’s population is foreign-born than LA’s.
Food depends a lot on what you go for. You won’t find much good Mexican food in London, but on the other hand, you can by a better croissant in a supermarket here than you can find in most of the US.
My experience is that until you get the concentrated areas you don't get the actual diversity of the foods. When you have large areas of the same culture you start to get regional restaurants from the culture, specialty restaurants from the calture, because the market is big enough and business needs to distinguish themselves. You also get the ingredients as there's a big enough market to import them. When you don't have the concentration you just get the generic representation of the food from that country.
LA is much less dense than London so maybe you need concentration for those things, but we don't. We don't really have monocultural ghettoes. The beauty of London is how dense and intermixed it is. Cheek by jowl, as Shakespeare wrote.
Food depends a lot on what you go for. You won’t find much good Mexican food in London, but on the other hand, you can by a better croissant in a supermarket here than you can find in most of the US.