Speaking in a Commons debate on social mobility last week, he told MPs that information, advice and guidance (IAG) services are in need of a "fundamental overhaul".
A survey commissioned by the independent panel on fair access to the professions, which Milburn chairs, found that 70 per cent of under 14-year-olds have never received careers advice.
Poor Connexions provision is to blame for this, he claimed.
"During all our proceedings and meetings and hearings, I have rarely heard a good word about the careers work of the Connexions service. I can only conclude that its focus on the minority of vulnerable young people is distracting it from offering proper careers advice and guidance to the majority of young people," he said.
But Steve Hoy, co-chair of the National Connexions Network, rejected Milburn's accusations.
Connexions is primarily a service for 14- to 19-year-olds, so rarely gives careers advice to under 14s, he said.
Where Connexions do provide IAG to young people, it is high quality and impartial, Hoy claimed.
"We know there are many young people and parents who put a lot of reliance on the IAG provided by Connexions. These comments could be very demotivating for the Connexions staff who deliver those services," he said.
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