Sir David took over as chairman last year after both the former chairman Marcus Agius and chief executive Bob Diamond resigned in the wake of the Libor scandal.
On Friday night Barclays board, in an emergency meeting, decided that both Bob Diamond and Marcus Agius should tough it out: they did not need to quit their respective roles of chief executive and chairman.
Stuart Walter, 23, of Lympsham, Nathan Goldfinch and Marcus Tancock, both 20 and from Weston, and Liam Grant, 19, of Cheddar all pleaded guilty to arson.