OK, I will try as a 'subject' of the system, but other people with different roles can probably tell you about other aspects.

The basis of the system is 'A' levels. People typically take 3 or more of these, with a final examination when they are apporaching 18. How these are assesed has varied over the years: when I did mine in the dim and distance past it was exclusively judged on a final examination. SInce then course work has been included as a way of determining the mark, but a few years back the Education Sectretary, Micheal Gove, changed it back, so it is now once again based on the examiniation.   Previously, these were graded from A though to F, but again some years ago and A* was introduced above the A grade.

The examinations take place in June (typically), with results out in August, and people start their University course late Septemeber or October. They typically go to University a week or two early to settle in.

As you can see, the timescales are quite tight, so most (all?) Universities start offering people places in June or July. Occasionally these are 'unconditional' but the vast majority are conditional: "We will give you a place if you get two A's and a B, or higher."   There is also a 'clearing system that runs from when the results come out to try and match students who either had no offer or did not meet the conditions with unallocated places in Universities.

So the whole system hangs of the examination results. This means that when the cabinet decided in March there would be no examinations it immediately created a problem, but as usual did not seem to recognise it. My approach would have been different: I would have said the examinates go ahead, even if we have to get hotel conference rooms and sports stadia and such spaces to get enough social distancing, and we have to pay for four or five times as many people to act as invigilators (people who watch over the students during the examination to stop cheating.) We also have to announce this is what will be happening back in March, so the students know. (As an aside, I was a bit surprised watching Newsnight last night that the editor of the Spectator, agreed with me, but there you are!)

Once you have decided not to have the exams, that gives you two choices. You can either try and change the entire system so it does not depend on examination results to allocate places, or you have to find a way of estimating the examination results. Bear in mind that the most reliable way - tested coursework - was scrapped a long time ago so you don't have that as a basis.

So this mysterious 'algorithm' was invented by someone (and we don;t know who) which basically said two things: the school will give more or less the same results as it has over the past five years or so, and, when the class sizes are small, the statistics are not reliable enough, so we will use teachers' assessments of what the grades would have been. That had the effect that pupils in private schools, which typically have much smaller class sizes, got the teacher assessments, whereas normal schools got the adjusted scores from the algorithm. As no details of the algorithm have been published it is hard to say how it worked, but it looks as if it lead to a 'rounding down'. It also penalised improving schools: one that has done better every year seems to have in effect the 'average year' as if it had not improved at all.

SO: the results come out. A proportion will have got the grades of the conditional offer even after the messing around. They are settled. However a proportion did not, especially if it a school where few students go on to University: there are reports of people expected to get several A's who where awarded D's, for example. So they lost their conditional place.

Over to the Univeristies now: Places like Oxford and Cambridge, and subjects like medicine are over-subscribed: there are few more people wanting to go there than places. Oxford, shall we say, now has a bunch of unfulfilled places because these people did not meet their tragt results. Time is very short, so they immediately offer them to the next people on the waiting list with good results. It is a statistical artifact of the algorithm that these are more likely to be from the private schools (because the teachers' assessments were used) than elsewhere. So they are given the place.

Now the U turn: everyone is to be given grades based on the teacher assessment. So the student from the ordinary place can now get the place? No, because it has been given to someone else. As it happens, it seems that the University has entered a legal contract in offering the place conditionally, so now both pupils have been offered the one place and are legally bound to be given it. So the University stands to be sued, or must magic up a way of giving both of them a place. This causes massive problems for places that are heavily oversubscribed.

And it causes problems for the rest. Durham University, for example, is one of the top in the country but historically has been a University where lots of privately educated students go who did not manage to get into Oxford or Cambridge. (There are many state school pupils as well.) So now there are all these privately educated pupils who are no longer knocking on Durham's door. Similar effects are happening with a lot of other other Universities.

All of this was utterly predictable the instant the government decided not to hold the examinations.