Herd immunity in this case isn't something you choose to cultivate or not. With such an infectious disease you're going to get it sooner or later; that's the UK's point. Trying to wipe it out through self isolation won't be globally 100% effective and if it's not it'll just come back. Ultimately only the population carrying lots of antibodies will end transmission for good.
I believe it's mistake to claim that the disease will inevitably become endemic in the fashion of the flu. It certainly reach that level but costs would be massively catastrophic in a multitude of fashions. Oppositely, that of the different nations who've contained the infection show that is possible to eliminate it from a region and so a world-wide effort could eliminate it world wide as well.
One factor is that the disease is much more deadly than the early commentators (notably in the Atlantic) believed and aside from making "everyone get infected, OK?" horrific, this gives a strong marker for the disease and a strong incentive to act.
This is a disease in which people can be infectious yet show no symptoms. How do you stop infected people moving between regions? Do you think a "world wide effort" is going to successfully encompass places like Africa, central Asia, even Latin America? It's out now, it'll be circulating for a long time.
(I've been doing the arithmetic for this stuff all day but here goes).
The UK's population is about 66 million. Sixty percent infected is 39,600,000. A 1% death rate (which, per above, you can't escape by "just infect young people" or something, jeesh) implies 396,000 dying. That many people dying, spread out evenly over a year is 1084 people dying per day but 10,840 people arrive sick at hospitals. Which is something the UK surely can't deal with. So with the health care system overwhelmed, the death goes to 5% or more and you have 2 millions deaths, much the WWII casualties etc.
Also, the "herd immunity" reasoning is wrong in the sense that we don't cultivate herd immunity to black plague, Ebola or small pox because they are deadly enough that we containment. Covids is in this special deadly "sweet spot" where it doesn't seem deadly enough to isolate in small area but too deadly to allow to run rampant across a city or nation. The answer that's forced on nation is mass city-by-city quarantine. Harsh but China's Wuhan experience was nowhere near the horrors that this "herd immunity" plan promises.