Stoker was put in charge two weeks after the Greater London Assembly appointed six trustees to the charity's board, including Murziline Parchment, policy director in the office of London Mayor Ken Livingstone.
The Charity Commission said the fund's current trustees were not permanent ones and that they were appointed because of their availability rather than their expertise. It said they would be replaced "at the earliest opportunity" by people who have experience in emergency and relief work, indicating that the fund is going to be a permanent entity.
The fund, which has so far raised more than £5m, made its first grants available last week. Families of those who lost their lives in the bombings will be eligible for grants of £5,000, and individuals who were admitted to hospital overnight as a result could receive £3,000.
Parchment said: "The full needs of the victims of the bombings and their families will emerge over time, but already there are many immediate costs."
The GLA said the fund's permanent trustees would decide how to spend any money left over after compensation had been paid.
Section 79 of the Charities Act 1993 allows local government to appoint trustees.