I said: "as the UK population approaches herd immunity (end June)."
Rehashing a previous post to do the maths again for 'approaching' herd immunity.
If we take 75% as the percentage of the population which need to be immune before that's achieved. With a UK population (over 4 years old) of 64M that's 47M. Currently about 15M have received the first dose and the daily rate is 435.310pd.
Once we've vaccinated 47M (first or both doses), we'll be over the 75%.
If the UK programme continues on plan/
past performance: assumes 400,000 a day from now on, and from 14 March split half and half (1st/2nd dose)).
14 Mar = 26M
14 Apr = 32M (roughly the number in JCVI Gps 1-9 btw, government suggestion/target = end April)
14 May = 38M
So estimate 27 Jun to hit 47M and approaching (effective) herd immunity (14 days later).
Caveats: Depends on
= vaccination programme continues at pace (400,000 daily and maintained, 7-day averages, less than current to allow for supply reduction and general pessimism bias

)
= how effective the vaccines are (we hope 90%)
= how infectious the viral strain is (come May) - factors into 'R' and NB it's going to be a lovely May (well last year it was

)
= restriction measures reducing R - these measures will have been progressively revised across the UK by then and
assumes vaccines minimises transmitting (as well as getting infected with symptoms) - emerging data suggest this is a reasonable assumption.
* A factor which would bring herd immunity forward is the number of non-vaccinated under 30s (about 20M all up) who have previously 'had' COVID-19, a good proportion asymptomatic and/or not tested, who still have sufficient antibodies to resist infection. Every million of those brings forward herd immunity 5 days.
* This ignores the cut-off continent and further afield, but only because this post is too long already.
One of the [benefits of] herd immunity is to keep vulnerable groups who cannot get vaccinated (e.g. due to health conditions like allergic reactions to the vaccine) safe[r] by making it less likely that they'll catch the disease.
Another is to minimise the opportunity for the virus to mutate and produce a variant either more transmissible, or more lethal or resistant to the immunising effect of the current set of vaccines.