I always have voted out of duty as a citizen to vote, but it always felt like a waste of time. The MEPs are unknowns you never see, and the proceedings are so divorced from regular politics that they seem like they serve little practical purpose in representing our views. Particularly when the people you are voting for are then members of supranational blocs with their own agendas. It's so far removed from the individual voter that it seems like they could do whatever they wanted and claim a mandate for it. I don't think democracy is particularly effective at this scale.
I think the Leavers were dissatisfied from the beginning. You can directly trace the formation of UKIP from the Maastricht Rebels. https://en.wikipedia.org/wiki/Maastricht_Rebels in the Major government.
UKIP was formed out of protest at what they saw as the EU going off in a highly political direction (i.e. becoming a lot more than just an economic area).
They may be wrong but the objections are based on fundamentals.
The EU might have retained popular respect with UK voters if the MEPs that the UK sent to parliament had voted in accordance with their electorate's desires rather than not-voted-because-they-are-a-protest.
Or not. Quite a lot of stuff in the media that is anti-EU, too. That might be more powerful.
I'm not sure what you mean by a tiny minority. IIRC the UK Parliament voted against Maastricht twice and it went through on the third attempt. I think UKIP has exploited and perhaps stoked the skepticism, but IMO did not create it.
As for polling, it looks like my memory doesn't quite match reality: http://theconversation.com/polling-history-40-years-of-briti...
This polling history shows wild oscillation over time, and the EU was formed from its predecessor just as things were close. I had been under the impression it was a gradual shift from the high of 1979 to the low of 2016.
Regardless, "stoked" sounds like a good description of UKIP's behaviour to me, so I think we may be agreeing with each other.