Most Brits I know were under the impression that it would stop or stem the flow of immigrants. They pulled the only lever they were given and it didn't work.
The funny thing is, even at the time it was clear that immigration would not decrease as a result of Brexit. Farage repeatedly stressed that it would open the door to greater immigration from the Commonwealth. People projected their own desire for lowered immigration onto the vote because, as you said, it's the only lever they were given.
Farage is making it very clear in this election cycle that he stands for reduced immigration. Do you mean to say that he has changed his mind?