The bad news is that it really is only a few, very select schools in a few, very select areas.
That's according to a new study by a researcher at King's college, which found state schools in the South East account for a surprisingly high proportion of students at Oxford and Cambridge Universities.
The research, by PhD student Sol Gamsu, found schools in inner London send 1.89 times more students to Oxbridge than the national average - closely followed by schools in the South East, which send 1.46 times more than average.
Meanwhile, those in the North East send 0.44 times fewer students than the average, while that figure for the North West is 0.57 fewer times.
Elite state schools
The study named so-called elite state schools, which act as "de facto feeder schools" for Oxbridge.
Around London, those include Sir John Lawes School in Harpenden, Parmiter's School in Garston, and Dame Alice Owen's School in Potter's Bar, as well as Watford Grammar School for Boys.
"Oxford and Cambridge cream off a handful of students from a large number of schools which are geographically distributed across the UK," said Gamsu.
"However, a small number of schools send much larger numbers of students, serving as de facto feeder schools to these two elite universities. In percentage terms, these schools sent 18 to 30 per cent of their cohort to Oxbridge in 2012-13. These are still largely the elite of the private sector, but this list also includes what have basically become elite sixth form colleges."
The study also named St Benedict's Catholic School in Bury St Edmonds, Thomas Mills High School in Suffolk and St Mary Redcliffe and Temple School in Bristol among the elite state schools.
The Downs School in Berkshire and the Cherwell School in Oxford were also among the top-ranking state schools.
Gamsu, who is due to present his findings to the Royal Geographical Society's annual international conference later this month, added that the rise of these schools isn't necessarily positive for the UK's state system.
"Much of the attention has been on the background of the students that Oxbridge recruits, but the way Oxbridge recruits remains the same: they still recruit large numbers from a small group of elite feeder schools," he said.