Hi PP
“From the perspective of the HI discussion, though, the only question that is important is does PCR massively underestimate the true number of infections? That is, is it likely that we have already reached HI levels, despite what the low PCR test percentage suggests?”
The way I see it…PCR overestimates genuine, traditional infections that relate to symptoms, risk and infectiousness.
The testing policy will underestimate the number of people in the population who would give a positive PCR result, because most people aren’t being tested.
These competing discrepancies are too large for PCR to meaningfully represent the number of clinically relevant infections. If you allow a ‘case’ as defined by governments to count as an infection that reduces to one discrepancy, so if you adjust for the proportion of people who aren’t being tested you might get somewhere in the precinct of the ballpark 
regarding ‘cases’. IMO that’s still not very useful.
I think we probably haven’t reached H/I levels, due to the still-high number of reported deaths (which should start falling soon as noted elsewhere, due to falling ‘cases’) - but I’m not sure, as it is possible that more and more are simply being labelled Covid because PCR is more and more likely to show evidence of past ‘infection’. In that case the only fully reliable evidence for the preponderance of Covid deaths must come from hospitals. This is a bit murky with its London-centricity and the known displacement of other serious diseases by Covid. At the moment I still buy into it more than not but there should be studies to confirm this picture is real before the world is turned upside down as a result of it.
This PCR problem is partially addressed by the ONS who do a weekly community survey, without using PCR but antibody tests instead.
This was widely reported:
In England, an estimated 1 in 8 people (95% confidence interval: 1 in 9 to 1 in 8) would have tested positive for antibodies against SARS-CoV-2 on a blood test in December, suggesting they had the infection in the past.
In Wales, an estimated 1 in 10 people (95% confidence interval: 1 in 14 to 1 in 8) would have tested positive for antibodies against SARS-CoV-2 on a blood test in December, suggesting they had the infection in the past.
In Northern Ireland, an estimated 1 in 13 people (95% confidence interval: 1 in 28 to 1 in 7) would have tested positive for antibodies against SARS-CoV-2 on a blood test in December, suggesting they had the infection in the past.
In Scotland, an estimated 1 in 11 people (95% confidence interval: 1 in 14 to 1 in 9) would have tested positive for antibodies against SARS-CoV-2 on a blood test in December, suggesting they had the infection in the past.
So maybe around one in nine, say, have been ‘infected’ or 11%. That’s just going by antibodies. I’ve seen several statements by researchers (who tend to know more than those on public platforms) that T-cell immunity is more relevant than antibodies, which not everyone produces (and presumably decline in some who had Covid early). The figure for those with a degree of immunity could be a fair bit higher. Say 50% higher, bumping it up to about 16-17%.
It’s worth re-readin your Yeadon 
as some of the populations had immunity without any prior exposure to Sars-Cov2 itself - maybe to Sars1 in the noughties or other coronaviruses.
This in particular
" Long et al (2020) find that almost half of previously infected individuals are no longer seropositive a few months later."
This suggests immunity would be underestimated by antibodies alone.
So H/I may not be miles away!?
It’s possible Yeadon’s confidence at the time was influenced by the low virus numbers in the Autumn but I assume his information is mostly sound.
Actually, it’s nothing like as bad as it sounds, and I’m surrounded by friends who’ve had it, or whose elders have, and who all report: no biggie, and usually pretty good results. It really isn’t any big deal. I’ve had arc-eye that was worse. All that-night discomfort (last night) removed by the soothing gel they gave me to take home, and all well today - the next morning. Thank the gods for the NHS!! Diolch yn fawr iawn iawn, Aneurin, ffrind da yn y nefoedd!