April already has Easter most years. My nomination for another Bank Holiday is Trafalgar Day in October. We need something to break the monotony between August and Christmas.
Trooping the Colour is the official celebration of the monarch's birthday. Edward VII changed the actual date to the second Saturday in June because his birthday was in November (like the present king) and it was cold and miserable, also when George V reigned it clashed with Armistice Day.
So...