This should probably be off topic but doesn't a hyphen join the pertinent words. So non-white British means all those people who have British residency/citizenship who are non-white? I think there are something like a million Poles (the people) in the UK but they'd be included under white British right? Or is there a separate category for EU types who are living in the UK?
I feel bad

steering off topic this far, but non-white British just means everybody who is not classified as "white British" (check Wikipedia for this classification that combines citizenship with ethnicity). Whenever completing employment forms or participating in the census, I (EU citizen in the UK) put a cross at "other white", certainly not "white British". My interpretation of the figures stands, imo.
Best wishes
StJohn