The 10 heads from Barnet, north London, face combined budget shortfalls of more than pound;2 million and have already warned the Government that their schools will be forced to close when the money runs out.
Now, in a direct appeal to the Prime Minister, they have written: "We feel certain that you would not wish to see our schools ruined.
"However, as we are more than two months into the current financial year, the situation is already desperate."
They want an urgent meeting with Mr Blair and say in their letter that previous correspondence with the Department for Education and Skills has met with "unhelpful" responses.
Barnet council has said it has no more funds to pass on to schools and last month commissioned an independent auditor to prove the point.
The heads, who have already made significant cuts, say the majority of them would have to make at least eight teachers redundant to balance their books, but are refusing to do so.