The EU has majority approval in every single member country and even the UK. In many cases, it gets 2/3 majorities.

Apart from survey data, there have been many referenda on EU membership or aspects of it over the years, with similar results.

Even for the most critical of countries, at the high point of anti-EU propaganda, opposition reached just a hair over 50%, which has turned out to be very unfortunate timing for the UK.

Edit: I had looked for, but forgot to include, the data: https://www.pewresearch.org/global/2020/11/17/majorities-in-...