From my understanding, the EU was supposed to be an economic partnership to facilitate trade. But I'm American and don't know the first thing about the EU. Still, I doubt the EU was the reason Britain had a democratic government.
Britbong here.
The EU is indeed that, but it is also a regulatory body that imposes the same laws upon every nation in the EU. This can be a good thing, like with EU consumer protection laws which protect customers from getting fucked in the ass by corporations, and they are pretty fair. But it's a double edged sword, like with the retarded cookie law (the thing where you get a notice from a website telling you it's storing cookies and wants to know if it's okay? Yeah... that was the EU's fault). Since the UK will be leaving the EU, there are concerns about whether these protections will remain, which laws will be kept, etc. There are some good laws in there, but there's also a few questionable ones, so eh.
The other talking point is about freedom of movement, a primary tenet of the EU which allows citizens to live and work in another EU country without needing a permit. This also relaxes travel restrictions between the countries; one of the nicest things to come of this was the Schengen area, an area within Europe that citizens can travel through without being subjected to border control. The Schengen area is opt-in for countries, and includes some countries that are not part of the EU.
Speaking of countries that are not part of the EU, there is the European Free Trade Association (EFTA) which was created as an alternative for countries who didn't want to join the EU or its predecessor, the EEC. Switzerland, Lichtenstein, Norway and Iceland (a former EU member) are all members of the EFTA. Because of this, they are not subject to the laws of the EU --- the ETFA is EU lite, per se.
Now, this is important because EFTA or EU membership is
required to be a member of the European Economic Area (EEA). Membership of the EEA is necessary to participate in the EU single market (with the exception of Switzerland, which has special agreements).
At this point, it is incredibly unclear whether the UK will remain in the EEA after their departure from the EU is ratified, and I have my doubts that they will be able to. For the UK to rejoin the EU single market, they will need to either a) be accepted into the EFTA and rejoin the EEA through that, or b) manage to ratify an agreement with the EEA a la Suisse.
And no, the UK and many other European countries had democracy way before the EU/EEC. The goal of the EEC was to establish cordial relations between European countries to prevent wars between states, and of course, boost the economy.