Ex-Labour leader Neil Kinnock has attacked city academies by saying they undermine fairness in education.
Lord Kinnock also expressed concern individuals or companies were being given influence over such institutions because they donated cash.
Academies were a "distortion of choice" because they allowed schools to choose pupils, not parents to choose schools.
But ministers maintain they drive up standards in areas where children previously were "denied" opportunities.
To become an academy, schools must raise up to £2m from private sponsors such as businesses or churches.
These organisations are then given a majority of places on the board of governors which run the academy's trust.
Lord Kinnock told BBC Radio 4's Today programme: "I am very evidently opposed to the multiplication of types of schools for the very simple reason if you get a multiplication of types you get a variation of preferences.
"It becomes a seller's market and what you then get is schools selecting parents and children instead of parents selecting schools.
"If you have a situation in which in exchange for providing about eight to 10% of total funding of school an individual on a trust or an outside body effectively gets control of the governing of that school - that's a distortion of choice and opportunity in UK education."
Lord Kinnock added that schools should have a mixture of all children from all backgrounds - "fundamental" to "high standards and equity and fairness".
City academies first began to open in 2002 and were designed to improve the performances of schools in England's inner cities, often the most deprived parts of the country.
Sir Clive Bourne, sponsor of Mossbourne Community Academy in Hackney, London, said Lord Kinnock should visit the school to understand what academies were doing.
There was a clear division between the headteacher, who dealt with all the educational needs and problems, and himself as a sponsor using his business acumen to ensures things like competitive supply prices, he said.
"This question of control, it's just not true," Sir Clive told BBC Radio 4's World At One.
Angela Eagle, vice-chairwoman of the Parliamentary Labour Party, said she backed the aim of academies: spending more money on areas that had been neglected in the past.
But she said cash sponsorship was not the only way to bring new energy from outside.
The government should look for other ways to boost morale in schools and motivate children, she said.