There's an ability distribution between private schools and the box-standard comp because most private schools require entrance exams so, from the very start, are selecting "brighter" children. However, I think this has only a small impact.
The fact of the matter is that children who attend private schools will come from homes where there is more of a focus on education and, as a direct result of everything that comes with this, more children from these schools are going to go onto the best universities. Besides, the gap between the best state schools and the worst is just as big a problem. If you banned private schools then the state schools in good areas would just replace them in all but name, and fees, and you would have the same problems.
It isn't a case that private schools are bad and state schools good - private schools are excellent, on the whole, and the reality is that they're much superior in many ways. Comprehensive schools should be studying their example to give pupils the same advantages that those at private school enjoy. We need to increase opportunity for those in the state schools and bring them up to line with the private and top state schools, not attack those which are working as they should be.