In what sense is the EU a foreign actor? The EU is a union of nations of which the United Kingdom is a member, and (up until it started to chop its own dick off) one of the most powerful members at that.
Germany 82,114,224
U.K. 66,181,585
France 64,979,548
Italy 59,359,900
Spain 46,354,321
So, yep. Most powerful being about 15% of the votes.
Still doesn't make the EU a domestic political institution.