I think it's unlikely that members skeptical of the institution itself would have much influence.
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.
Those skeptics certainly started skeptical, but they were also a tiny minority. I was thinking about the people who they convinced to side with them, and how UKIP's refusal to participate in any meaningful way may have created the evidence they needed to convince people the EU wasn't listening.
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 just don't think many people in the UK in general (not just Parliament and the media) like the EU. I spoke to a lot of people who voiced anti-EU sentiment but voted Remain out of fear of the consequences. I remember there being just as much if not more dislike in the early 90's after Black Wednesday.
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.
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.
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.