Jeremy Corbyn had an 'unfair educational advantage' and was still a scholastic failure

Having a private education is often described by those on the left as having an unfair advantage, it's one of the arguments regularly made against grammar schools. 

It's interesting to note that the Labour Party leader, Jeremy Corbyn, went to an independent Prep school, Castle House School, and then Adam's Grammar School. So with these educational advantages Jeremy Corbyn must have achieved higher A-Level results than otherwise and gone onto a good university. Actually no; Jeremy Corbyn left school with a paltry two E-grade A-Levels and did not go on to university. 

Maybe having a private education doesn't bestow such an advantage on those who receive one, or maybe Jeremy Corbyn was just too thick to be able to take advantage of the superior education that he was privileged to receive. 

If the Labour Party somehow managed to win the next General Election would Jeremy Corbyn be the least well educated Prime Minister of the United Kingdom?