Referendums are seldom used in the UK. This one was not legally binding. Legally a referendum only has the effect that Parliament decided. In this case: none.

Referendums are seldom used in the UK. This one was not legally binding. Legally a referendum only has the effect that Parliament decided. In this case: none. Parliament is sovereign and it voted to leave the EU. Its decision was informed by the referendum but it was not bound by it, nor did it have to take any action at all. The decision was political because it was untenable politically for Parliament not to vote to leave the EU considering the referendum's result.