People were lied to about Brexit

It is possible that the people advocating Brexit have no idea about how businesses operate or how finances actually operate. Because if they did they would not have voted for Brexit anymore than they would have taken a knife and slit their own throats.

This type of person who isn't educated about basic economics or finance is also the type of person voting for Trump here in the U.S. Representatives and Congress people and Senators who are Republicans are refusing to vote for Trump because he would economically destroy this nation or militarily destroy it the same way that Brexit may destroy England's economy now. Cameron is not invoking Article 50 simply because he doesn't want to go down as the Prime Minister who completely destroyed England's economy. However, by offering to have this vote you could say he allowed the people to be bamboozled by ignorant or self serving leaders similar to Trump in the U.S. and thereby is somewhat guilty of the outcome.

Trying to get people who know nothing about economic matters to vote correctly is difficult in any nation. Half the time they are going to cut their own throats because they just don't have enough knowledge about actual finance and businesses and how they all work and interrelate together with government to make a useful decision that might (with the wrong decision) completely destroy their lives and all they hold near and dear.