May I ask why people are desperate for a 'social mix'? It sounds very noble but what practical advantages does it bring a child, and why don't you think you get it in an independent school?
I would say that the social range is fairly much the same in either sector, but you have a shift.
When my children were in their primary school, we were probably on the top of the SEC scale, but now we are all private, we are close to the bottom (not the very bottom though). There are just as many families above us now as were below us before (all measured by salary and parental education, not birthright).
Assuming independent education is a valid choice for your family, why is it better for the "social mix" to be skewed below you in terms of SEC indicators rather than above - which is pretty much the reality of those who can just afford independent.
Is there really the great English, pythonesque, need to look down on people?
Personally, I would much rather my children could experience a lifestyle to aspire to, rather than only experience complacency.