Except... not really. :-)
The two main parties campaigned against changing from FPTP because the status quo suits them. Even their insistence on calling it "AV" was intended to imply that in FPTP we already had the "gold standard"; so why change? Proportional representation, a system where you get parliaments that actually reflect the broad spectrum of public opinion, is anathema to the two big traditional parties; especially the Conservatives.
The Conservatives have been able to pursue policies that benefit their core (minority) support while visiting austerity on the majority. A more diverse parliament, where they didn't have absolute power and would have to broker a consensus, would rein in their more neo-liberal tendencies. So that's hardly a plus for FPTP.
It's also clear that a lot of people voted "Leave" in the referendum as a protest vote assuming that, as with general elections, their votes wouldn't make any difference in the great scheme of things. Ironically, a vote where there are only two choices is the one instance where all votes really do count under FPTP.