Or maybe rephrased the outcome for vax'd 85+ and generally speaking, old fat and sick, patients is so vastly better that anaphylaxis among that group would be a rounding error, being vax'd for those people is like 800+ times better than unvax'd. On the other hand, for thin healthy kids the hospitalization rate for covid for a couple months is about the same as the anaphylaxis rate in that age group, so vax'ing healthy young people won't reduce hospitalization rates overall, instead of having like 1 per 100K kids in the hospital for covid you'd have about 1 per 100K kids in the hospital for anaphylaxis, so for them the risk is vastly reduced from no improvement to some improvement if they watch them for 15 minutes.
Therefore the best policy would be some sort of age based triage. Not-old, thin, healthy are more likely to end up with anaphylaxis hospitalization than covid hospitalization, so put them in observation for 15 mins to minimize the damage from vaccination. As for the old, fat, and sick, the rate of anaphylaxis hospitalization can seems to be about one thousandth the rate of covid hospitalization so proportionately observing them for 15 minutes won't save as many as simply vax'ing more of them would save, so push them thru the assembly line and don't bother with the 15 minutes.
I don't know the ratio of old/fat/sick to healthy in the UK. Perhaps, similar to some areas of the USA, may as well simply make one policy assuming everyone is old/fat/sick or some combination. In that situation the UK plan might make sense. Like in the USA having a vax clinic at a nursing home or Walmart or similar, just assume everyone attending the vax clinic is old/fat/sick.