3 of 16Adverts Those other 17 countries not in the European Union include ourselves! Why fly an organisationâs flag that we are not involved with? Remainers should check the Brexit referendum result from 2016. Good marketing move by the EU, first to casually appropriate the name of the continent, then to appropriate Europe Day. The first Europe Day was on 5 May, 1964. It was held by the Council of Europe to celebrate that organisation and its commitment to human rights, democracy and the rule of law. Then along came the European Communities, the EU at the time, and they thought we will have that, their first was in 1985. The EU does hold Europe Day on a different day from the Council of Europe.