"This is your decision. The government will implement what you decide," a pamphlet issued by the government at the time said.
That's basically saying: the current controlling party promises to try to implement solution the majority of voters decide.
However, they should have to have a vote of Parliament to push through a change of the legal structure of the whole country. Seems absurd that they'd be able to by fiat just wipe out all the regulations by which the country runs without Parliament agreeing on the record.
As a US citizen it also seems strange to make such a huge change by simple majority. Parliament and all other political and legal decisions are made using representative voting. Every U.K. election I watch from afar amazes me in that the left parties generally get far more cumulative votes that conservatives but the Tories somehow skate away with a majority in Parliament. Everyone seems ok with that but then a 2% majority of the 72% who voted is enough to scrap 40+ years of legal progress by numerous elected Parliaments? Very strange.