The letter, seen by Third Sector, calls on the board to "put the case for our funding to be restored with the same passion and commitment that the team has shown in these difficult circumstances".
It continues: "As trustees of the foundation, we trust that your commitment to securing the promised financial support will be unwavering."
The foundation faces closure in 2008, a year earlier than originally planned, after it did not receive the first of two £1m payments it was expecting from the Camelot Group last month (Third Sector, 3 October).
Brooks said the trustees were working hard to broker a settlement with the Camelot Group, which recently won the franchise to run the National Lottery for a third time.
"There is ongoing discussion between the trustees of Camelot Group and the foundation," said Brooks.
"I understand that staff are extremely concerned because the foundation is coming to an end."
After receiving the letter, Brooks met senior staff at the foundation to respond to their concerns.
