It's looking increasingly unlikely that herd immunity is a realistic aim.
Ro is the R number with normal behaviour and no immunity. The formula for the fraction needed to be immune to reach herd immunity is (Ro-1)/Ro
The original variant had an Ro of ~3 but the new variants are said to be ~50% more transmissible.
If R ~5 then the fraction needed to be immune is ~80%
The vaccine is unlikely to give "sterilising immunity" ie complete protection against transmission, is not 100% effective against disease either, and reduced effectiveness against variants has been reported for some variants. Given that we're also not going to be immunising children, then reaching a complete suppression of the virus through herd immunity doesn't seem likely.
However, it's still vital as many people as possible are vaccinated, not just to protect themselves, but also because even if we haven't reached formal herd immunity, outbreaks will be much easier to contain the closer we are to that limit. There seems to be a body of opinion that current immunity levels reached through prior infection and vaccinating have helped speed the reduction in cases in the current lockdown, and that level was probably something like 20% at the start rising to maybe 30% now and over 50% in the next couple of months.
It may be that we end up similar to the flu; there's an annual booster jab but still outbreaks through the winter, dying down in the summer but never completely going away.
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