will UK unis accept a degree mostly from non-traditional sources?

[rvm]

rvm, what does your daughter want to study?

Sociology, psychology or neuroscience. 

We know UK universities don't do Gen Eds and that she needs to select a "major" and basically stick with it throughout her 3 years at a university in the UK.   Because of this, I'm trying to convince her to get her undergraduate degree in the states then apply to graduate schools in the UK.  She wants to get her undergrad degree in the UK so that the 3 years at the uni can be applied  to the total number of years she needs to live in the UK in order to apply for residency.