The UK could surely apply BI only to their citizens. California would have more trouble, given the 14th Amendment, though might be able to do something similar to what we do with schools, requiring that you live there a certain amount of time before you start receiving BI.

This is assuming that the influx of population actually would be a bad thing, though, which I'm not sure of one way or the other - I see some arguments on both sides that hold at least a little water.