As a non-privately educated yet still straight A student, I have always walked past my local private colleges ( Trent college and Nottingham boys high school) and just felt depressed, how lovely the grounds are, good condition their sports facilities, and just the learning environment of being surrounded by like-minded people who want to get good grades rather than " mess around" every lesson compared to the education that I've received.
Now that I'm in year 13, I've sort of come to realise that it gets better at university as everybody has the same opportunity ( apart from oxbridge which has a vastly disproportionate amount of privately educated students).
In the end it is only a disadvantage if you allow it to be one, anybody going to any school can get straight A* GCSE's and A levels if they spend enough time working, it's just that those that have been fortunate enough to have had a private education have had the comfort of doing that work in a more pleasing environment and often with teachers educated to a higher level - my chemistry teacher for AS read Biology at university, not the best.