Without a vaccine it will take quite long to reach herd immunity (if CV remains the same):
Let's say UK herd immunity is 66% of persons infected.
That would be 44m cases for UK.
Let's assume the true number of UK cases is 2m, as an example. Remain 42m to be infected.
Even if we would allow 5,000 new cases any single day from now on
it would take about 23 years to reach 66% HE:
5,000 x365 days x23 yrs = 42m.
23 years. Would you think more than 5k per day is within NHS capacity?
Would it be possible at all to keep R=1 at 5k without overshooting??
We can scrap all those HE theories and just hope for a vaccine.