In a statement issued today, Sir James Munby, president of the Family Division, said the court system is struggling to cope with the demands being made of it, adding that there does not appear to be a strategy for addressing the situation.
In August, a total of 1,254 applications were received by Cafcass, an increase of 34 per cent compared with August 2015's total of 941.
Not only was this a record month-on-month increase, but it was also the third month in a row the total number of care applications has exceeded 1,250 - a total that was only reached for the first time in June this year.
Annual numbers of care applications have already nearly doubled in the past seven years - from 6,488 in 2008/09 to 12,781 in 2015/16.
"We are facing a crisis and, truth be told, we have no clear strategy for meeting the crisis," Munby said.
"The immediate implications of this crisis are twofold. First we have, at least in the short-term, to struggle to cope with our existing resources.
"Second, these very large increases in the number of care cases are, inevitably, driving up very significantly the cost of legal aid."
Munby said the reasons for the increases in care applications are little understood, and although investigations are under way, much more research on the issue is necessary as a matter of urgency.
"The fact is that, on the ground, the system is - the people who make the system work are - at full stretch," he said.
"We cannot, and I will not, ask people to work harder. Everyone is working as hard as they can."
Munby said that increasing emphasis must be placed on initiatives that aim to solve problems early rather than dealing with them once they emerge.
He cited family drug and alcohol courts (FDAC) and the Pause Project, which works with mothers who have had children previously taken into care to try and prevent repeat removals, as examples of work that should be continued and expanded.
"FDAC, Pause and similar projects are, at present, the best hope, indeed, in truth, the only hope, we have of bringing the system, the ever increasing numbers of care cases, under control," Munby said.