The head teacher of Brighton College has written to state schools in Brighton and Hove inviting them to send him their bright but poor pupils.
Mr Cairns sent the invitations because he wants to extend a scheme that he set up with Kingsford Community School in Beckton, East London.
The Kingsford scholarships give a potential route out of poverty for up to three pupils a year.
And in the past week Brighton College has announced that one of the current Kingsford scholars, Issah Abdul-Moomin, 18, has been offered a place at Oxford University.
Last year one of the first intake from the London comprehensive, George Weller, won a place at Cambridge.
Isaah has been offered a place at Lady Margaret Hall, the Oxford college once attended by the Education Secretary Michael Gove.
He will study philosophy, politics and economics (PPE), the same degree course as Prime Minister David Cameron and Labour leader Ed Miliband.
The Sunday Times yesterday contrasted the toll of violent deaths among Kingsford pupils with the number of students at Brighton College going on to Oxford and Cambridge universities.
But it also cited Issah praising his teachers at Kingsford for helping him to pass 14 GCSEs, seven at A* and seven with an A grade.
Brighton College has just announced that a record 18 pupils so far have received offers from Oxbridge colleges, including twins Peemdej and Peemtat Utsahajit.
Of the Kingsford scholarships, Mr Cairns said: “This innovative scheme has already enriched a number of inner city children’s lives and we will be extending it next year to include more schools.”
“However, I remain convinced that the government needs to create an elite sixth form academy in every city in England to provide an environment in which academic rigour is valued, where only ‘hard’ A-levels are taught and where sights are definitely focused on applications to top universities.
“There are thousands of Issahs in our country and schools like mine can only offer a lifeboat for the few.
“We should offer opportunities for many more than that.
“I have written to Michael Gove to propose this – though his office is notoriously bad at replying to any correspondence.”