Great question. I perused Wikipedia a bit, and it seems like the relevant event would be the UK joining the European Communities, which eventually transformed into the EU. The UK government directly decided to join, but a referendum was held two years later, and "stay" won with 67% of the vote:

https://en.wikipedia.org/wiki/United_Kingdom_European_Commun...

The formal entry into the EU was done with the Maastricht Treaty in 1993 and didn't have a referendum, but it was basically a direct continuation of their EC membership. Although I imagine someone opposed to EU membership might argue that this was the most important point, and the people did not have their say in it.

The EU has evolved over the years. The UK joined the EEC (a predecessor to the EU) in 1973. In 1975, there was a UK referendum about whether to stay in the EEC, where 67% of voters chose to stay. Since then there were a number of treaties which expanded the economic and political reach of the EEC, including the Maastricht Treaty, agreed upon in 1992, which was when the EEC became part of the newly formed EU. Whilst some countries held a referendum over the Maastricht Treaty, the UK was not one of them.

Since 1992, it could be argued that the biggest change to the EU was the Lisbon Treaty. You can read more about it here.

https://en.m.wikipedia.org/wiki/Treaty_of_Lisbon

To be clear, between 1975 and 2016 there were no UK referendums on EU membership, so technically yesterday's vote was the first time the UK public was consulted about being a member of the EU. In contrast to the EU, the EEC was much smaller in scope, though it's clear that the architects behind the EEC always intended it to become a much bigger political player.

"There will be no peace in Europe if the States rebuild themselves on the basis of national sovereignty, with its implications of prestige politics and economic protection…. The countries of Europe are not strong enough individually to be able to guarantee prosperity and social development for their peoples. The States of Europe must therefore form a federation or a European entity that would make them into a common economic unit."

Jean Monnet, 1943

https://en.m.wikiquote.org/wiki/Jean_Monnet

https://en.m.wikipedia.org/wiki/Jean_Monnet