My understanding is that the elite don't want Brexit because it will derail their gravy train. As to peoples' indifference, your contention is easily disproved by the numbers voting.
My own view, for what it is worth, is that from Parish Councils to the EU, each layer of government takes a slice of our taxes. Less money for the things that matter to us ordinary mortals, schools, hospitals, social care etc.
Please note that Scotland, Wales, & N Ireland already pay for an extra layer. Scots in addition already pay an extra 1p on Inco Tax. The Northern Ireland Assembly, suspended for 2 years, presumably still pay Members & Staff salaries, after losing millions on the 'Ash for Cash' scandal. Perhaps there are savings when the lights were switched off.
A sobering tax fact is that despite our sending around a net £350 million a month to the EU, the total tax take in the UK is at 35%, one of the lowest in Europe. The French pay 57%!!!