Hummus - I totally agree. As my username indicates, I voted leave. I voted leave because of the democratic hole at the centre of Europe that is the European commission (and I used to work in Brussels, so I do know how it works, and I also know that other European countries have raised worries about this, most notably in the German parliament recently). I'm also old enough to have despaired of any chance of reforming the commission.
But I certainly don't have any issue with immigration, or free trade - nor (if Ashcroft's poll the day after the referendum was to be believed) do a lot of other leave voters - about half listed "sovereignty" as their primary reason for voting leave, only 1/3 listed "immigration" as their top reason. (Now I'm sure a large fraction didn't have a clue what sovereignty means - but I'm pretty sure a large fraction of remain voters couldn't tell you what the main parts of the European decision making system are either... there's ignorance on both sides).
And I really do want the decision to invoke article 50 subject to as much parliamentary scrutiny as possible. May and Rudd seem to have gone off on a crazed "pander to the bleakest possible set of interpretations of what the lowest common denominator of the British electorate might want from Brexit" crusade if the Tory party conference was any indication. They're whipping up a level of xenophobia and racism that is frankly horrifying. And their view of how to conduct negotiations seems to be based round finding the strategy most likely to leave us stranded in the economic wilderness for decades to come, and they seem ideologically wedded to this strategy. So I want parliament to scrutinise their proposals and come up with the best way forward. This isn't the same as reversing the referendum result. This is to do with ensuring that decisions are made properly and rationally.
I also want parliament to scrutinise things because the whole bloody reason I voted the way I did is that I want democratic accountability, not decisions taken in back rooms far away from the scrutiny of parliament, whether that's the MEPs in Brussels or our own parliament here.