Actually, the electorate voted a tory government into power several times. That is all they did. The referendum was an advisory referendum only, it was the governments decision, backed by parliament, to leave the EU. Or did you see 17 million signatures on the letter invoking article 50? Governments can disregard advisory referendum outcomes if they think those are stupid, trust me, i have seen that several times now over here.
The EU had certain red lines of course, same as the UK, but always left the choice on what to do to the UK government. It was the UK governments decision not to stay in EURATOM (an entity independent, but closely aligned with the EU), same as it was its decision to leave EASA. And that has led to the current mess with licenses. And yet again, EASA makes it as easy as possible to get an EASA license for UK license holders, without much base in treaties and hard law, trying to help as much as possible. No help at all of course is forthcoming from the UK government, not that anybody would expect that in the first place.