https://en.wikipedia.org/wiki/European_Union_Referendum_Act_2015
The European Union Referendum Act 2015 (c. 36) is an Act of the Parliament of the United Kingdom that made legal provision for a pre-legislative referendum to be held in the United Kingdom and Gibraltar, on whether it should remain a member state of the European Union or leave it
"This act required a referendum to be held on the question of the UK's continued membership of the European Union before the end of 2017. The bill did 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."
Thats the (Uk defined) legal basis of it, which makes it even very questionable as a tool for a consultative indication imho if you get a 52% result on a 72% turnout.
Basicly, what i'm saying is that obviously the British people are not all that much in favour of Brexit as the Brexiteers for obvious reasons would argue, that atleast shows from the lack of expedience by which Brexit is being resolved, because the logic atleast is that "Brexit should be easy to resolve providing enough support for a given sollution", and it figures when reviewing what (within UK's political context) the referendum was really about and how it should be reviewed given that specific outcome vs turnout. Furthermore any talk of a goverment uwilling to implement the result under these circumstances is "putting things on it's head", in principle the authority of the HoC is far above the referendum which they allowed by that act.