The UK's strategy is apparently based heavily on the principle of "flattening the curve". This isn't the approach taken by other nations that have imposed heavy quarantine measures relatively early in their outbreaks, such as Italy.
As far as I can see, the following are the fundamental assumptions of this strategy.
1. Much of your population will get infected at some point. This is unavoidable.
2. Heavy quarantine measures as employed in various other countries are not sustainable or effective over the necessary timescales. The quarantine will need to be lifted after a few weeks to avoid all kinds of other negative effects (including those adversely affecting health in other ways) and then the exponential spread will resume anyway.
3. Certain parts of your population are at much greater risk than others, due to age or other complicating conditions. These are the people you most need to protect. Most other people will be able to look after themselves at home with some unpleasantness and inconvenience but relatively little risk of more serious or permanent consequences.
4. Someone who has previously been infected and survived will have a degree of immunity thereafter.
5. There are limited intensive care resources available in the NHS to care for patients in more serious conditions.
6. As time passes, several things improve likely outcomes:
6a. We move past the winter season, which both reduces stress on the NHS generally and also somewhat reduces the effects of the coronavirus.
6b. The NHS is increasing its number of intensive care facilities above normal levels.
6c. Eventually, antiviral medications and vaccines become available, but widespread availability is likely to be at least a year away.
So the plan is to allow a degree of natural infection within the general population spread out over time, with the aim of keeping the number of more serious cases at any given time within the capacity of the NHS to treat as well as it can.
As this happens, we buy some time for the situation as a whole to improve, and there is also likely to be some degree of herd immunity building among the general population. In the meantime, the priority is to minimise exposure for those most at-risk and to ensure as much as possible that anyone who does get infected with more serious consequences can at least be treated as well as possible.
In probably a few weeks, when the level of general exposure and the number of more serious cases have risen and we're in danger of reaching capacity limits in the healthcare system, then we start to deploy the stronger quarantine measures and the like, for the same reasons as everyone else but in the hope that they serve the purposes above in particular.
People who understand the science much better than I do seem to be saying that this actually is quite a reasonable strategy and really could work better than what other nations are doing as long as those assumptions are broadly correct, but also that it does have some specific risks, such as the fact that we aren't 100% sure so far that surviving an infection really does confer some degree of immunity, and the possibility of deferring the peak until it hits the more dangerous winter season at the end of this year.