Re: Of course the original referendum is only "advisory" it is not legally backed.
Of course, a majority DIDN'T vote "out" - only 37.5% voted "out". Conversely, only 34.7% voted "Remain". The correct statement is that 51.9%, OF THOSE WHO VOTED, voted to leave the EU.
A more correct strategy for referenda is to count the non-voters in some agreed way. Typically, they may represent "status quo", or other proportion. This would then be used to set a benchmark point at which the result carries validity. It may be that the valid pass mark was then 60% or 65% in either direction as seen appropriate.
Nigel Farage tried to make this point in a rather cack-handed way by suggesting that if the outcome was close, "say less than 5%", that a second referendum should be held. Clearly he's gone quiet on that now as he has the result he wanted.
But parliament can still make a suitable judgment on whether they agree that 37.5% does indeed represent the "majority" view and choose to accept or ignore the result.