Every secondary school should have teachers who attended elite universities, Lord Adonis said today.
The former schools minister said it was "very difficult" to get pupils, particularly those from poorer areas, into top universities unless their teachers have studied at those institutions too.
Addressing the Independent Academies Association (IAA) conference in central London today, Lord Adonis said: "You need a good mix of teachers, of course, at any successful school, but you cannot be a successful school unless you at least have a certain proportion of your teachers who have themselves come from leading universities in to which you intend to send your best students."
He added that in his experience it is "very very difficult to send students on to top universities unless you have a certain proportion of your teachers who come from those universities themselves.
"Far too many schools, a good proportion in the bottom half of comprehensives, and still quite a few academies have no Oxbridge teachers and very few from leading universities."
Lord Adonis, who served first as schools ministers and then as Transport Secretary under Labour, said he had been taught by a teacher who went to his university, Oxford, who knew how to navigate the process and inspired him.
Teachers who have attended top universities know how admissions work and have good specialist subject knowledge, he said after the conference.
According to the latest official figures, just 40 poor students (those on Free Schools Meals which is a measure of poverty) went to Oxford or Cambridge last year, out of 80,000 who were eligible.
Lord Adonis warned delegates it would not be possible to transform admissions to top universities "unless you can develop a cadre of teachers in your own schools that have that background themselves."
Academies, and other secondaries, should do "whatever it takes" in terms of dealing directly with institutions, or signing up to Teach First.
Teach First is a scheme that trains top graduates from elite universities to teach in challenging secondary schools.
The scheme is recruiting 800 teachers this year, and this will grow to 1,200 by 2013/14, Lord Adonis said, meaning one in ten of all new teachers in secondary schools will be Teach First recruits.
Lord Adonis said there needed to be a "dramatic increase" in the number of academy students going to university, especially elite institutions.
This is the "biggest single development, above all others, that will transform social mobility in this country", he said.
He cited the example of Mossbourne Community Academy in east London which has helped 10 of its students to win Oxbridge places this year, saying there was "no reason" why others cannot do it.
Lord Adonis warned that the academies programme must expand rapidly because there are "still too many under-performing schools."
"We need to see many hundreds more academies and we need to see them over quite a short period of time," he said.
"Time will not wait. Every year that we leave these schools which are seriously under-performing, not delivering the goods, that is another generation of kids who are failed and its another big handicap to social mobility."
Lord Adonis, who was a pioneer of the academies programme under Tony Blair's Labour government, also repeated his calls for every university to sponsor an academy.
"Universities are always by definition the most successful and highest aspiration education institutions in the country," he said.
Speaking afterwards, he added: "The Government needs to be in dialogue with every university about sponsoring an academy and be prepared to help facilitate it."
At the moment a "handful" of institutions, including Nottingham University and University College London (UCL), have agreed to academy sponsorship.
Academies are semi-independent state schools, which receiving funding direct from Government. The programme was established under Mr Blair to transform under-performing secondaries in poor areas.
The new coalition Government extended the programme to allow any primary, secondary or special school in England to apply for the freedoms. There are currently around 400 academies.