What follows is my observation and understanding and if something has very recently changed or I am simply wrong then I would be pleased to know.
You can attend proceedings and, through online access to the schedules, track the "real time" progress of individual cases through the system (but not by looking for specifics but instead only by systematically trawling through all the listings). But, in my experience, after the event courts in the UK are very opaque by comparison with practices elsewhere (but not everywhere) in Europe. In some countries transcripts of entire proceedings are permanently accessible online - perhaps not all (exclude such things as family related stuff) but lots of them - and quite a lot of detail in general is essentially open and available on application.
In the past I have asked for assorted (UK) court information, for example particular statistics (which by definition are entirely anonymous) and also more specific things. On every occasion I have been rebuffed with things varying from the old chestnut of data protection through "we don't keep that information" to bluntly being told that I could get nothing unless I myself was involved in the case. Even when someone is/was involved in a case, they cannot reliably get transcripts of anything (even when they were noted) unless very soon after the event and only ever later if, in the lucky event, they were preserved. In short, (in the UK) the proceedings themselves are usually open but immediately thereafter everything increasingly becomes a closed secret.
This is entirely in line with the sort of secrecy which is part of much/all of institutional life in the UK. To the best of my knowledge all court information has now for many years been recorded in digital form so it exists within the system and is therefore very easily retrieved at the proverbial click of a mouse.
This is not to say the information is truly locked away within the court vaults - oh, no. While individuals cannot buy their way into the data banks, certain commercial interests can. Credit agencies make commercial agreements with the courts and they get unfettered access to the chapter and verse details they want - and then sell them on every time they provide a credit report. And then there is the murky relationship the courts have with the media. So much for data protection.