Didn't Nigel Farage say himself a second referendum would be required if the results were close. 48-52 was the figure I remember.
Pretty sure live on air on voting day he said the same when he though leave were loosing around 12am.
Cameron repeatedly stated that government would support the outcome of the referendum, even if it was a pass of just a single vote.
And in the end there was 1.2 million more leave than remain votes. that is a fair size city's worth of people.