Number of points I can add as an ADI.
There is no block booking. There has never been block booking. It has never been possible. One licence number with a valid theory is one test. That's it - there's no clever work around, no clever cheat that anyone can use.
We (ADIs) don't have the system sewn up as a PP suggested. We cannot book tests for someone who doesn't have a valid theory. We cannot book a test for someone who already has a test booked. As above - one valid person, one test.
Bots have been largely been tackled. The biggest mechanism of abuse has essentially been closed, the ability to swap tests between learners, to do this you now have to call the DVSA which makes automating a 'cheat' with bots impossible. There are still cancellation finding services, they are making a substantially over the top profit, but they are simply automating what you can do yourself - regular checks of the public facing booking system.
Driving tests have increased by something like 20-25% over the last few years. I think the last figures I saw were something like 1.9 million per year compared with around 1.5 million in 2019.
Staff retention is poor so it's very difficult to increase the examiner base. The basic pay is similar to a NQ nurse or teacher (and you may well feel that figure is too low for those groups as well, but that's another thread). The difference is that most DEs join the industry midlife whereas most NQ teachers and nurses would join the industry at the start of their working lives. Salary expectations when you are 40-something tend to be higher than when you are 20-something. Furthermore the typically later start in the industry (and you'd like examiners to be highly experienced drivers, right?) inherently means that even for committed staff their potential lifespan in the industry will be relatively short compared with other fields leading to greater staff turnover.
The biggest reason I suspect for the increased demand is one that the Government and DVSA have not admitted publicly and is nothing to do with Covid for example. What else happened to coincide with the end of Covid? Massively increased immigration to the UK (a very quick google for some data suggests around 2.5-3 million net immigration since 2020). It doesn't matter what your political view on it is, this has meant huge numbers of people who want to be able to drive in the UK have suddenly been added to the pool of people.