Wealth doesn't seem to be an explanation here. Her father was a welder and her mother was a nurse. She went to a grammar school and got there by merit.
I don't think that being poor on TV or radio means you are not intelligent.
In other words, I think it's easier for an intelligent person to look stupid on TV than it is for a stupid person to get a degree from Cambridge. Neither is impossible. I'm just talking about likelihoods.
Basically what I find objectionable is the lazy or conceited assumption that someone who has views you disagree with must be unintelligent.
In all the years watching Portillo with Abbott I've seen him make fun of her and talk about their time at school together. I don't recall him implying she is unintelligent.