This is from Full Fact
A referendum can be legally non-binding but, arguably, politically binding.
fullfact.org
The
European Union Referendum Act 2015 didn’t say anything about implementing the result of the vote. It just provided that there should be one.
In other countries, referendums are often legally binding—for example, because the vote is on whether to
amend the constitution. The UK, famously, doesn’t have a codified constitution.
A UK referendum will only have the force of law if the Act setting it up says so. In practical terms this would mean someone would be able to go to court to make the government implement the result. The
Alternative Vote referendum in 2011, for example, was legally binding in this way.
So the European Referendum Act 2015 was drafted in such a way as to make the result of the referendum ''non binding'' and as the result was close and the number of non voters approx a third of the voting population the ''politicians'' could've refused to implement.
A more sensible approach would've been to put a minimum vote requirement of say 60% of the population (the same way the unions are treated) or a requirement that all countries in the UK union would have to vote leave (but that would be possibly more divisive.