It gets worse - looks like the PCR problem affected tests between 8th September and 12th October.Looks like at least some of those odd - LFT says positive, PCR says negative - test results are related to problems at one of the testing labs (where the PCR samples get sent). Tests done between 3rd and 12th October in some parts of the country may be affected.
https://www.bbc.co.uk/news/health-58921280.amp
More details, to follow later today apparently.
From what I've read so far, it seems to be tests done at local testing centres in some parts of the country - in particular Berkshire and to the west.
UK public health are estimating 43,000 positives were missed on PCR. Hopefully the people with symptoms stayed home despite the positive PCR. More likely they took the result literally and went back to work/school/uni and round to their gran's as normal.
I suspect we'll see a guidance change about how seriously to take a LFT positive.