Sir James Munby said the system was "ill-prepared" and facing a "crisis".
Official figures show care cases have more than doubled in the last decade to an estimated 14,713 in 2016.
Sir James said it was "generally agreed" that the Baby P case in 2007 was behind an initial rise.
Peter Connelly, referred to at one stage in court as Baby P, was 17 months old when he died at home in Haringey, after suffering months of abuse.
The toddler had suffered more than 50 injuries, and had been visited 60 times by the authorities in the eight months before his death.
The serious case review put Peter's "horrifying death" down to the incompetence of most of the staff members of official agencies who came into contact with him.
In comments made public on Tuesday, Sir James made what BBC correspondent Clive Coleman called a "blistering assessment" of the care system.
Calling for urgent research, he said: "We are facing a crisis and, truth be told, we have no very clear strategy for meeting the crisis".
Charting the rise in cases, he said there was a "dramatic increase" of some 35% in cases in 2009-10.
He noted: "It is generally agreed that this unprecedented increase was the consequence of the Baby Peter case".
Yet the number of care cases continued to "increase significantly" even after the initial reaction to Baby P.
Sir James said that research into the reasons for the increase was needed "as a matter of urgency".
Care cases, with their potential for life-long separation of children and their parents, are of unique gravity and importance, he said.
Fairness and justice demand a process in which both the parents and the child could fully participate with the assistance of representation by skilled and experienced lawyers, he added.
Sir James stressed: "I do not believe that child abuse/neglect is rising by 14%, let alone 20% a year.
"So this cannot be the sole explanation.  It follows that local authority behaviour must be playing a significant role."
The number of cases in which children can be separated from their parents on the application of a council has seen a "relentless rise", says the head of the family courts in England and Wales.