It isn't really in the short term, because for herd immunity to have a noticeable affect on reducing the number of infections you need a large percentage of people to be immune. We're not going to get that large percentage in the next few months, unless we have an unimaginably grim death toll. Having say 1 million people infected and recovered in the next few months would see a lot of people die, but would still provide less than 2% of people immune to the virus, so it wouldn't stop it spreading.Herd immunity is effectively taking place whatever your strategy because it is a natural thing.
But your post quoted a claim that it was the UK's approach. Our government say it isn't, and regardless of it being a natural thing, it's not going to happen and be successful.So it isn’t anyone’s approach
It's possible that the best solution will to be to restrict contact (restrict, not full lockdown) for the whole year (until a vaccine is available), unless the weather can help. But allowing the population to contract the virus, in some misguided idea that we'll get herd immunity, will not be a success story.but it will have an effect one way or another depending on the approach i.e. some approaches may mean immunity is reached further down the line that enables a quicker return to normality. If you go full Wuhan lock down, you face the situation of a month of severe restrictions, then what...only 50k of 11m are now immune and if you lift restrictions likely the epidemic will grow again.