He has a plummy voice and therefore is judged as being privileged, self important. Many people have plummy voices and are normal working people. He went to private school -this gives pupils confidence, they do public speaking and debating, to make it easier for them later in their careers.
This is the same as judging someone from Liverpool or Newcastle as thick because they have a regional accent , or every cockney must have market stall or drive a Taxi. He may be 'posh' to some, but I think more people would trust him to represent the UK than the blond baffoon we have at the moment.