And how long can they keep strict containment in force, and what happens when it lifted? You're speaking as if China or SK are now magically immune from a second wave as soon as they relax their restrictions.
In this case the science is flat out unsound: There are several coronaviruses known to infect humans. None are known to result in lasting immunity, and some are known to not result in lasting immunity. This is one of the challenges in making a vaccine.
Given the observed hospitalization rates, many millions in the UK will require hospitalization due to corona. At the moment, their hospitals could support merely thousands. We know from other cities that the mortality rate (particularly among younger people) is dramatically higher when adequate medical care is not available.
Under the UK's argument, the worst outcome of aggressive mitigation is that you are actually successful at it and achieve containment which just shifts the infection later in time at a high economic cost. Given the existing known infection rates in the UK that seems unlikely at that point, but even if it were to happen it would provide time to ready treatment facilities and allow for the discovery of more effective and/or scalable treatment techniques.
Fortunately, the UK has been backing off from its initial position and has now been recontextualizing their position as 'mitigate as much as possible'-- which is what pretty much all of the west is doing.
Except in Hong Kong, Singapore, Taiwan, or (more arguably) Japan. And South Korea, while they had a rougher early outbreak, seems to have gotten a lid on the disease now.
That's not really correct. Containment certainly can work. Whether it will or not is still an open question. Right now no western country has been able to match that. Italy, Spain, France and Germany are probably out of time to try. But the UK is still relatively early on its curve.
So, for that matter, might the UK "infect the herd" trick. The science isn't unsound, though it's not nearly certain. So the risk management is just crazy and I can't understand it either. But... it really might work.