Speaking in America, Gordon Brown said: "I am determined that everything we do, the inquiries we are having in this case, reveal everything that went on.
"But I am absolutely sure that, like me, every parent in the country is outraged and shocked by what has happened and angered about what happened to that infant."
The shadow children's secretary, Michael Gove, has accused ministers of not doing enough despite being told of alleged failings in Haringey Council.
Both were reacting to news an employee raised concerns about child protection six months before Baby P's death in August 2007.
Baby P was 17 months old - his mother and two men were convicted of causing his death at the Old Bailey.
The DCSF has confirmed it received a letter dated 16 February 2007 containing allegations "that child protection procedures were not being followed in Haringey".
Local Lib Dem MP Lynne Featherstone wants a public inquiry and says someone at the council should take responsibility.
No-one at Haringey Council has lost their job over the case.
The council welcomed a government review, saying it would be "open and co-operative" with inspectors and would implement the findings "swiftly and comprehensively".