If the Brexit vote is treated as binding, a simple majority will have been given exceptional power over a country and generations of its citizens.
From Geoffrey Robertson in the Guardian:
Our democracy does not allow, much less require, decision-making by referendum. That role belongs to the representatives of the people and not to the people themselves. Democracy has never meant the tyranny of the simple majority, much less the tyranny of the mob (otherwise, we might still have capital punishment). Democracy entails an elected government, subject to certain checks and balances such as the common law and the courts, and an executive ultimately responsible to parliament, whose members are entitled to vote according to conscience and common sense.
Many countries, including Commonwealth nations – vouchsafed their constitutions by the UK – have provisions for change by referendums. But these provisions are carefully circumscribed and do not usually allow change by simple majority.