So you think that 'English' family will have a genealogical tree populated by only English, going back hundreds of years? Really? No Irish, Scottish, French etc? How many generations are needed for someone to be called 'English'? What percentage of genes can be from other ethinicities?
I bet there's plenty of people that you know and consider English who had ancestors that were from different countries.
And I haven't got any sense of entitlement. In fact, I don't even live in the UK- I might move there in the near future, as DP is English (although, wait, I think his family originated in France 1000 years ago and there's some Irish blood there as well, so perhaps he's not
).
What I do know is that if someone in my country had a greatgrandparent who was foreign-born I would not view him as not Polish. I very much doubt she/he would, either.
Perhaps you see a lot of Poles who have recently emigrated to the UK, looking for work. Their English in most cases is not perfect, they don't feel very confident in their new surroundings, they tend to keep together. But are you really saying that their greatgrandchildren shouldn't consider themselves English (or Welsh or Scottish), especially given the fact that after intermarrying with English there won't be that much Polish blood left, anyway? That obviously goes for other ethinicities as well.
And finally, ethnicity doesn't have much to do with love for the country you were born in, espousal of that country's ideals, culture etc etc.