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I'm not sure that they ever really did that much. If at all.
A significant number of Europeans really did. The U.K. used to have a reputation for good sense in some areas (and nutty attitudes in others). Just to pick one example, there's long been a significant number of French people living in the U.K. and enjoying career opportunities that were harder to achieve back home.
On a bigger scale, Britain going blatantly senile has left some EU politicians who used to ally with (the saner) UK politicos more exposed.
I'm not sure that they ever really did that much. If at all.