Like I said yesterday: it's a cliff-hanger. Let's see what @soniasodha has got for us on Monday.
My recollection: the UK's modeling at the time was catastrophically wrong - "UK 4 weeks behind Italy, and 5-6 days doubling time."
That's on the record (and it was wrong).
These numbers seemed to come out of @neil_ferguson's model. Then some model assumption was changed, and estimated deaths became more realistic (500,000). No one knew why because the model code was unpublished. It seemed like robustness hadn't been checked.
I remember someone claimed the change was due to previously underestimating hospitalizations by a factor 2. I found that strange because the pandemic was growing by a factor 2 every 2.5 days. So healthcare system collapse would just move back or forth by ~2.5 days.
Why is 500,000 deaths realistic? You don't need a model for that: Covid-19 is said to kill about 1% of those who catch it. Maybe 2%. If the whole UK population is infected, 1-2% die, or 500,000-1,000,000, order of magnitude. Not everyone will get it, so ~500,000 seems ~right.