We started lockdown on 24 March. If you assume that it takes 1 month between infection and death, that would mean the losses of life since 25 April all happened due to people catching C19 during lockdown. That number is ~9000 people.
Assuming a CFR of 0.5%, this means that about 1.8m people caught the disease since the start of lockdown in the space of 16 days.
I know that this is very much a rough and ready estimate, but that means about 100k people caught covid-19 every day on average during lockdown.
If the r0 continues to hover around 1.0 and the rate of spread stays about the same, it'll take around 14 months for the UK to reach herd immunity. Obviously, r0 might drop as people become more knowledgable about the disease and adapt their behaviour. But that could be cancelled out as the overall number of infected increases and/or the populace becomes increasingly complacent about distancing. It's too early to say for certain how things will turn out. But looking at the way Brits have handled lockdown so far, I'd lean towards the latter scenario being the overriding factor.
If we want to save lives, we need to isolate the vulnerable. If we want to end the crisis, we need to reach herd immunity. Luckily, those two solutions aren't necessarily mutually exclusive.