This is a very MN discussion not to focus on the WP angle. This boy sounds remarkable. A FSM pupil with a year 12 A star already in the bag and more predicted? That's a feat.
More unis don't interview because, no matter how Oxbridge may try to control it, interviewing tends to advantage the already advantaged group.
DS's friend applied to similar unis with all A star predictions and all 8s and 9s at GCSE. Again only got an offer for his last choice until, at the 11th hour, an offer from Warwick came in. Prior to that, he was planning on reapplying.
It sounds a bit unfortunately Katherine Birbalsingh to suggest working class pupils should put up with lower levels of aspiration. Nothing wrong with reapplying with grades in hand.