Private schools feed into the top universities because the private schools provide actual education. The problem isnt that private schools are too good or that private schools educated people get better grades.
The problem is that the majority of pupils in state schools, be they intelligent or not intelligent never stand a chance and are recieving a terrible formal education.
Are you prepared to devote the resources necessary to provide class sizes in 'state' schools in the UK that match the class sizes found in private (i.e. 'Public') schools?
I am, many are not - in the timeframe of an election cycle it is wasted money. The money spent today would only show positive returns in 10-20 years time.
State school in the UK costs the governement £7,100 a year per pupil vs £13,700 a year for private schools (averages). The government is getting poor value for money, but it would cost ~50bn a year to send every secondary state school pupil to private schools.
It is cheaper to simply pander to your base, make the next generation of their offspring dumber and blame the foreigners or the rich people or boats or whatever gets people angry. It actually increases the size of your political base, with the only downside that it dumps your future party with a massive social welfare bill in the distant future. By then they will be burying you at a state funeral, and your decendants will be living offshore somewhere nice talking about how great the country was back in your day.
The problem is that the majority of pupils in state schools, be they intelligent or not intelligent never stand a chance and are recieving a terrible formal education.