The "herd immunity" approach is a dangerous gamble, as one of the big unknowns is "How long is the immunity after recovery from COVID-19" -- it can be anything between 0 (no immunity) and infinity (immunity for life). If acquired immunity holds for less than the time required for a vaccine to be widely available, "herd immunity" will quickly become a massacre. The first wave will knock off the medical system (even if somehow everyone over 60 is protected), ensuring that the second wave will be devastating.
I much rather prefer the South Korea/Singapore/Japan alternative to the UK one.
The race is to arrest the exponential curve, somehow, at any temporary cost, for if we don't we can't apply the working options for COVID-19 response from Japan, South Korea, and Singapore.