I've lived or spent extensive periods of time in most big European countries (Germany, UK, France, Spain), and there isn't much hate between them anymore. Maybe in the 70+ age bracket you will find some. Then you maybe have some mild distaste from 50-70 year olds, indifference at 35-50 and some appreciation from young people. If you compare German, French and British opinions of each other with their opinions of Turks, North Africans, and Indians respectively it's not even a contest.

That doesn't mean that anyone's going happily hand over their sovereignty, but the picture you are painting of Europe does not fit with my experience at all.