Sorry, long time lurker here.
37% is enough though because Parliament said they would honour the result
You've said it three times now, Bowchicawowow and I can't ignore it any more. Parliament did not say they would honour the vote. The idiot Cameron did and he was not Parliament. He wasn't even constitutionally entitled to say it.
This is what Parliament was told about the EU referendum in House of Commons Briefing no. 7212 . This was the information given to MPs about the Bill they were going to vote on.
This Bill requires a referendum to be held on the question of the UK’s continued membership of the European Union (EU) before the end of 2017. It does not contain any requirement for the UK Government to implement the results of the referendum, nor set a time limit by which a vote to leave the EU should be implemented. Instead, this is a type of referendum known as pre-legislative or consultative, which enables the electorate to voice an opinion which then influences the Government in its policy decisions. The referendums held in Scotland, Wales and Northern Ireland in 1997 and 1998 are examples of this type, where opinion was tested before legislation was introduced. The UK does not have constitutional provisions which would require the results of a referendum to be implemented, unlike, for example, the Republic of Ireland, where the circumstances in which a binding referendum should be held are set out in its constitution.
I can't give a link because it's a download but it's easy to find. Just search on House of Commons Briefing 7212 The information is towards the end of the document under 'Types of Referendum'