I would say that I worry lateral flow test results are being double-counted with the lab checks, except that it would be good news because cases would be lower than they look as would positivity. I strongly suspect it's a double-counting error that will be discovered soon.
Uni anecdata: DN got tests done at uni no problem for going home and said they were contacted to ask if they'd take them; they aren't retesting all the previous positive cases so that's a small percentage who don't need tests. The larger impact on student numbers is probably that such a huge proportion of students already went home at the start of lockdown and didn't go back. All but 3 flats in DN's block had gone home, those flats (including DN's) were unable to because they were isolating due to one or more cases in their flats.
Regarding London and Tier 3, it doesn't make sense to me to have boroughs in different tiers, people will just walk into the next borough to shop. If it were only cases in one small part of London with Met police enforcement then it could work, but not the way the cases look now.