It's not "only available" to the top 7%. Two parents on just above average income could pay for private education, and a lot do. I know tons of families who could afford private education, but they'd rather spend their money on other stuff. That's fine, but you can't then moan that you feel like kids who went private have advantages. I'm sure yours also benefitted from the £15-20k you didn't spend.
If both your parents are doctors and you live in a leafy suburb with 2 annual foreign holidays, an outstanding state school, and every extra curricular you've ever fancied doing, you'll probably have just the same options in life as your parents' colleagues' kid who lives in a less nice area, rarely goes on holiday and puts the extra funds into private school. The first family isn't somehow less privileged than the other because they made a different choice.