Well Ireland was 95% Catholic, and had a terrorist guerilla war and seceeded from the UK in 1922. This often happens in Europe when there are ethnic disagrements (latest example: Kosovo). Or there's policial independence movements (e.g. Catalonia, Scotland).
Or is there still discrimination within categories of whites?
With regard to Polish people, there has been a lot of Polish migration to UK in the last few years since Poland fully joined the EU. So there'd be loads of "white Polish" families who moved there in the last 10 years. Not exactly comparable. There would be racism against ethnic Polish people. The UK does have a large Indian and Pakistani population, some third generation by now. And yes there can be racism against them. I suppose a pedant would claim the US racial definitions are still relevant by claiming things are different, but social and legally racism against Polish people, and Pakistani people would be seen as quite similar, not different types of discrimination. "They took our jobs" would a common type of discrimination in the UK against "white" migrants from Eastern & Central Europe. Racism between, what in the USA would be considered, "whites" does happen in Europe.
Do the info pages for individual schools in London prominently display "country of origin" information, so white British can ensure they don't accidentally send their kids to a school that's 90% white ethnic Polish? http://www.cps.edu/Schools/Pages/school.aspx?SchoolId=609951.
Or are Poles in London seen like say Jews in the U.S.? Sometimes the butt of a mean joke or nasty comment, but otherwise not situated fundamentally different from the majority group?
Remember, Europe and the USA are different and have had different histories. Europe has had a slightly different history of racial discrimination than USA. The have literally been wars.
I don't have an encyclopedic knowledge of European social conflict, but I don't imagine there is a lot of catholic versus protestant tension in say London, nor do I imagine there are persistent and massive socioeconomic disparities between the two groups in London (or at least nothing comparable to the more than factor of 2x disparity between blacks and whites I cited for Chicago).
And running with your example, what do you imagine would have been the political situation in the U.K. if say London had consisted of 60-70% Irish nationalist Catholics in 1985?
Or is there still discrimination within categories of whites? Are Londoners whose families originally hail from say Poland still dramatically disadvantaged compared to ones who can trace their origins in England for centuries? And if so, what would the politics be in the U.K. if London consisted of 60-70% of these hypothetical disadvantaged poles?