This phenomenon is the subject of well deserved exasperation, but it is also just a bit of a riddle. It's well known and understood why delaying restrictions is harmful on a policy level (more people get sick, measures are in place for longer etc etc). What's less clear is why the government doesn't seem to understand this. What's driving these mistakes? Is it just stupidity, or is there some tangible gain, political or otherwise, which is accrued from these delays? I'm not sure I have the answer, but here are some possibilities I think are worth considering, some mutually supportive and some mutually exclusive.
1. Stupidity. I've always assumed that even ministers of this government by in large understand the nature and dynamics of this crisis (the basic ideas aren't particularly complicated!), and I'm pretty sure Matt Hancock does, but you never know. They are certainly under a lot of pressure from backbenchers and activists who really are stupid enough to not understand what is going on.
2. Blind optimism/motivated reasoning. This may be what drove reluctance to push for more control measures in the Autumn, when it is rumoured that Sunak and Johnson fell for some wilder ideas pushed by Gopta and Heneghan that the herd immunity threshold was already fairly close, perhaps due to cross immunity from other coronaviruses. This appears to have been largely an exercise in wishful thinking, as does the strong assumption that transmission from schools is negligible (there is good reason to think it may be lower in children than adults, but the belief that it was near non existent was probably largely just what people wanted to be true). Perhaps there is a similar kind of blind optimism that delays introducing lockdowns.
3. Blind pessimism. I think this is less important now, but in the early days of 2020, this was probably the crucial thing that prevented European countries from mimicking the success stories of East Asia, Australia and New Zealand. Quite simply, there was a widespread belief that it was naive and unscientific to think that the spread of the disease could be controlled to any meaningful extent (remember people arguing that the Italian government was being a bunch of crass populists by introducing a lockdown?). This kind of pessimism seems deeply inappropriate now (controlling covid in the short term is clearly possible, and vaccines are here, now!) but bad ideas have long shelf lives. Measures that are continuously too late can feed into this pessimism; we act to late, we do far too little to isolate cases when they are low, and people start to tire of measures that don't seem to work well enough. Moreover, the new strain certainly does raise questions about whether the measures the British government thus far been willing to contemplate will suffice (at no point have we closed non essential workplaces to the same extent Italy, Spain or France has).
4. Public opinion. I don't think this is a real constraint on the government, but it is worth mentioning if nothing else in its negative form as this is frequently cited as a possible motivation for delays. Polling has consistently shown substantial majorities in favour of tougher restrictions sooner than they were announced, across the political divide (see here on school closures, for instance). I suppose you could still have a noisy group that opposes restrictions, and perhaps the government finds it convenient to be forced to act (probably why they tend to leak measures to select journalists hours before they are announced, so people are not hearing the measures from them the first time). There could be a bit of a bet that compliance to measures will be higher once people are afraid (i.e once the situation is obviously bad). But I don't buy that this can be a significant factor. It would make far more sense politically to bet that an already broadly supportive public would reward successful policy making.
5. Poor management style in government. This for me is probably the most convincing part of the explanation. This government seems to favour a management system whereby individual ministers understand their brief to be about representing specific interests which they lobby for. The Prime Minister understands his job as an arbiter between these competing interests. Sunak lobbies for the Treasury, Hancock for the Department of Health, Williamson for his education priorities as they understand these. This is a uniquely bad way of running things in a situation where there are significant feedback loops and effective policy making relies on understanding the dynamics of a system of moving parts. The Treasury has come to understand (or feels it has to understand) its position as in conflict with covid restrictions, even though they are not. Williamson feels he has to lobby for schools to stay open, come what may, even though nowhere in the job brief for the Minister of Education did it say that better educational outcomes should come at the expense of large amounts of death. Still, this explanation does require a little bit of explanation 1. or perhaps something similar, as you'd expect that intelligent ministers would realise the interdependence of their departments and the mutual benefit of just going for maximum viral suppression. At the very least, competent leadership from the Prime Minister would enforce this view. Which brings us on to point 6.
6. Incompetent and weak leadership. Lockdowns may be necessary, but in the short term, they do have significant costs associated with them. These are hard decisions to make, particularly if you aren't that comfortable with thinking about mathematical and scientific models. Even if there is no gain from delay, incompetent and weak governments may simply put off decisions until they are out of options, as they are so put off by the short term costs that they end up just paying much higher costs when they are forced to.