I have more time for your average "non native" British person who fully embraces British culture than I do your average "native" British person, I get a feeling of great pride when I see people of all colours waving the flag, or doing things that you would consider "British"
As for people who make no attempt to integrate in the slightest, I don't give a **** about them, and I wish they weren't here.
Simple as that. I think many people are more than willing to accept people from different cultures, and we should be multicultural, but revolving around one culture.
I know it's hard to say exactly what "British values" are, and people obviously love to make fun of Tory politicians when they say that but it is disingenuous, people know the sentiment of what they mean, and in my opinion it really is something that should be encouraged.