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I think that's a real stretch to assume a wicked skew for no apparent reason. Anyway, I tried plugging your numbers in including assuming that from the current 50% infected, there were still anothe 9k who unfortunately will die.
If you then need the remaining 240k deaths from the remaining 50% population, this means that the death rate will have to be 120x the current one if the herd immunity level is the government stated one of 60% (Only 40x if you choose 80% as the required herd immunity level, and 24x with no herd immunity)
Sifta
They're not mutually exclusive, both could still be correct. Neither necessarily contradicts the other.
For example, the 50% of the population that are suggested to be infected could be very heavily skewed towards the under 70s which would explain the current low number of deaths.
(Also, the death rate in the UK is doubling every 3 days. Since there were 57 deaths today then if that rate continues there will be ~1450 deaths in 14 days time, which would be from the currently infected group, and some ~6750 more will die between now and then. This is still a long way off 125,000 though.)