If we are talking Brexit, the exact result was
Leave: 17,410,742 votes (51.89%)
Remain: 16,141,241 votes (48.11%)
Margin: 1,269,501 votes (3.78%)
Turnout: 72.2% (33,577,342 votes cast)
So minimum number of voters needing to switch sides to have swung the outcome is 634,751 people
That represents about:
1.89% of votes cast, or
roughly 1 in every 53 voters who participated.
Plus Farages admission that had Remain won, it would not have stopped there - he would have argued for a rerun based on "how close it was".