Surely, it's not about education level, but messaging - which the tories own. They can come up with things that are simply not true; and get enough repeats of it, and have it unchallenged (in public view) that it sticks and hurts.
Labour (and Lib Dem, and Green and...) can't get genuine scandals to stick.
The owns the media - including the BBC now; the right owns fake news.
"education" plays a part - but only really in terms of critical thinking skills, and remaining skeptical in the face of mis-information, and having your prejudices pandered to.