There is some misinformation here.
AIC 76/2003 already contains a General Permission for charity flights providing you comply with the conditions in the AIC. You do not need specific permission from the CAA.
Only if you want to move outside of the conditions contained in the AIC do you need specific permission from GAD. We do this for the de Havilland Moth Club Charity Weekend at Old Warden each year and GAD are extremely helpful and very forthcomiong. Yes, they need a bit of time, don't ring them the day before.
HTH
VA