Seven per cent of the UK population went to private school. But, for years, Parliament has massively over-represented this demographic.
It used to be far worse, though. Back in the 1979, around half of all MPs from the main three parties had been to private school. That included nearly three quarters of Conservatives and more than half of the Lib Dem MPs. Labour has always had a far lower proportion of privately educated MPs, but it has nevertheless remained significantly above the 7 percent national average. According to research by the Sutton Trust, the figures are slowly becoming more representative of the population. Among the current(2017) crop of MPs, 29 per cent are privately educated.

52% went to comprehensive schools, and 17% to grammar schools.
Over one in ten of the privately educated MPs went to Eton.
87% of MPs are UK university graduates, 24% went to Oxford or Cambridge, 30% went to non-Oxbridge Russell Group universities and 33% went to other universities in the UK. Approximately 10% of MPs hold a postgraduate qualification.
45% of Conservative MPs were privately educated, down from 48% in 2015. 15% of 2017 Labour party MPs attended an independent school, down from 16% in 2015.

https://www.telegraph.co.uk/news/general-election-2015/politics-blog/11498660/Revealed-how-many-General-Election-candidates-have