Why do you think Jeremy never aimed high education wise?
He was gifted in mathematics.
I think gifted is a relative term, in an age where O Levels were the gold standard. He certainly knew his parents were wealthy, and how much was being expended on Sheila, and the future possibility of private education for the twins. His interest in geography also came in useful, as he fatefully studied the terrain between Bourtree Cottage and White House Farm. In the back of his mind would be the location of his place of birth.
To answer your question more directly, I doubt the stuffy atmosphere of Gresham's did him any favours, with far more chalk and talk lessons than hands-on experience. To his credit he did move on to Chelmsford College after the relative failure at the previous institution, buckling down to work after sensing Nevill's disappointment at his academic performance to date. But by this time he had realized what he was to inherit, and I think the spur and motivation to continue serious study was lost.