People were lied to. Some of them believed the lies.
Borris and Farage said that £350m will go to the NHS. Here's a picture of Borris by a sign that he had created for his campaign:
https://twitter.com/mgtmccartney/status/746245181532418048
It says "Let's give our NHS the £350 million the EU takes every week"
Here's a picture of their campaign bus:
https://twitter.com/mgtmccartney/status/746245181532418048
That says "We send the EU £350 million a week
Let's fund our NHS instead"
What have the Brexit campaigners said the day after the referendum?
Here's Farage explaining that saying it was a "mistake" to say the £350m per week would go to the NHS.
https://twitter.com/GMB/status/746218028195426305