Many a turning point in history has been decided by a margin smaller than 48%. For instance, the American referendum to use German as their official language (instead of English) was defeated by a narrower margin; and the French referendum to keep the Franc (instead of adopt the Euro) was defeated by a narrower margin. But:-
Our Referendum was flawed. We are told 16 Million voted Remain 17 Million voted Leave; but nearly 18 Million where disenfranchised. 13.1 Million UK Citizens living abroad according to F&C Office, 3 Million EU Citizens living in the UK who because of their rights under 2004/38/EC and its predecessors have established a life here but have had no need to take up British Citizenship, 1.6 Million aged between 16 and 18 who have the most at stake, and several thousand confined or too infirm for their vote to be validated.
Secondly, the conduct of the Referendum was flawed. The Government has no rules or regulations for conducting Referendums; instead runs them as if they are Elections. (The two are very different.) – Parliament approved a “franchise” which included UK nationals who where resident overseas for less than 15 years. However, the Government procedures only allow for UK nationals who have previously registered to vote in the UK (those turning 18 while abroad are excluded); and who follow a complicated procedure of continuous registration and re-registration. At least 71% of UK nationals living abroad did not know of their obligations under this re-registration procedure. In other words the Government ignored Parliament and made up their own rules.
Furthermore, the well documented failings in the procedures that allow UK residents to vote, which includes EU nationals living in the UK, disenfranchised many EU nationals in the 2015 general election and will have contributed to the voice given to the Leave lobby. There were also well documented failings with the postal vote system in 2015; and a few anomalies in 2016. – Can we have any faith in the Electoral System, and especially the Referendum process at all?