Blend the mayonnaise, egg white and cracker crumbs in a mixing bowl. Add the crab and fold gently without breaking up the meat too much. Shape into 8 equal patties. Coat with breadcrumbs, pressing them into the surface.
Melt the butter in a large frypan and place the crab cakes in. Turn to coat them with butter. Place under the grill and cook, turning once, about 5 minutes or until browned.