I don't think that numbers can be written off as false positives on the LFD tests.
You would expect similar numbers of false positives with similar number of lateral flow tests.
Look at these dates a week apart, with the number of tests (approx) and the number tests not confirmed with a PCR, then number confirmed.
8th March: 1 500 000 tests (approx) 837 positives: 419 confirmed
15th March: 1 514 000 tests (approx) 915 positives: 554 confirmed
22nd March 1 067 000 tests (approx) 1595 positives: 85 confirmed
Now if you assume that all the 837 positives on 8th March were false positives then that's approximately 0.055% false positives.
For 22nd March 0.055% gives approximately 595 false positives. So 1k. over that.
So I think there could be a tentative conclusion from that, that there has been some spread in school. However, hopefully the LFD tests will have removed a good number from the schools before they spread it, hopefully slowing the spread down to a level where it doesn't get out of control again.
It does seem odd that such a lot of the 22nd haven't been confirmed. It would be interesting to know how many people are going for the PCR test. I wonder if a fair number haven't bothered because either they know someone has already tested positive of their contacts (which must reduce the likelihood of a false positive, plus they already have to isolate) or they're thinking that by the time they've got a result, it'll be pretty much the end of term-ours finish next Tuesday.