It's simple really. People vote to cut welfare, thinking they'll never need it. People voted to leave the EU thinking (probably rightly in most cases) that their job wasn't dependent on membership. (I'm not sure if anyone did research in Sunderland to see any difference between those who worked for Nissan and, say, those worked in Wetherspoons.)
Plus people who were never going to work again voted massively to leave and those who hadn't started work didn't get a vote.
But Leadsom was lying. Leave Without A Deal would not have won the referendum.