Zufan, clearly you've touched on a sensitive issue. I'm suspecting that your overall culture shock has more to do with your concern with safety than with this notion of a 'true' Brit. I'm going to stay something a bit controversial here, but if you are white and find yourself in an area predominately not white, then you may find yourself uncomfortable. I used to live in inner-city Baltimore. I was mugged by an African American young adult on crack. It took me ages to not suspect ANY young black man of not having similar intentions. I hated this about myself. Logically, I knew that the person passing me in the street was more likely to be a talented jazz musician from the top music school down the road than another potential mugger, but psychologically, it took me time to get back to normal. While you haven't had a mugging, you've clearly seen signs of crime in the nieghborhood and coupled with your overall emotions about moving, I think (and hope) that this is what you are really driving at.
That you came from San Francisco, is in my opinion, helpful, but only marginally. London is still a completely new place so comparisons aren't necessarily that helpful.
There are posts in this forum that do talk about areas in London that are safer/more diverse/more affordable.
To be blunt, it seems you obviously haven't been paying much attention to British news while preparing for your search. If so, you would have seen loads of stories about the diversity of London as well as many stories on the pros and cons of immigration. I'd also like to point out that just because a group of non-white people are dressed in non-Western style clothing and speaking a foreign language does not mean they aren't first, second, third, or even fourth generation British born citizens.
I also lived in Newcastle and not only is there a large Asian population, but also seriously deprived white working class neighborhoods. You'd feel just as uncomofortable there and those are 'real' Brits.
Take care and I hope you can get more settled soon.