My memory is kind of fading w.r.t. what exactly happened in London, but I seem to recall their plan was pretty much explicitly "let's embrace COVID so we can get herd immunity"?
Herd immunity was England's plan initially - until they ran the numbers.
Then they looked at a new model and realised that if they achieved herd immunity, the predicted number of people who would die, this summer, was going to be massive.
They also realised that some of those deaths would be due to the healthcare system being unable to treat a lot of people, making the number who would die even larger, and avoidably so. Presumably hospitals turning critical patients away would also be socially & politically disastrous. This started the "flatten the curve" strategy.
So they rapidly did a U-turn towards progressively increasing lockdowns, and now decreasing restrictions.
Now with a bit more thinking behind us, we also realise herd immunity might not even work as predicted, because it's not clear what are the long term effects of the virus, including immunity and ability to be infectious to others after new exposure despite having had the virus before.
Like in the USA, people aren't complying with much consistency, and it looks obvious that many people, mostly younger, don't care to protect others. The emerging anecdotes and data about long term damage when surviving do not seem to bother them either.
Nonetheless, it looks like the strategy has made a large difference to the outcome compared with what early models predicted if there were no restrictions.
And now with the emerging data about long term harm (including evidence suggesting asymptomatic carriers who don't know they had it but may have sustained organ damage affecting them in future), we can be confident the strategy, by reducing the numbers of people who get it, will have made a difference to more people than previously thought.
This doesn't stop a few people from saying that the lockdown was unnecessary because there were only X deaths and the temporary new hospitals were not much used, when X is because of lockdown (and is larger than the models predicted). There are people with no brain apparently.
It seemed that way (I'm not certain it wasn't just incompetence in realising how quickly it was spreading). Then they did strict lockdown and worked hard to shield the most vulnerable. The shielding was poorly executed - like everything the UK government do.
They had 'spread the curve' type measures (stay home if sick and 'use common sense' etc) for 10 days. The infection rates carried on doubling during that time.
London is a perfect example of how quickly this thing can spread in a modern city and how many people get sick at once. The only reason the death rate wasn't way higher is that many many people self isolated for their own protection in early March.