what pedagogical magic increased the five stout GCSE pass rate from ~40% to ~80% in two decades?
I don't think it did, did it?
The figures for the past four years for five including English and Maths were 59%, 59.4% 59.2%, 53.4%.
The crazy high figures quoted between 1997 and 2010 related to (a) 5 GCSE not necessarily including English and Maths and (b) the use of a variety of crazy "equivalent" qualifications which were, bluntly, worthless.
O Level pass rates had gone up to around 40% by the end of their use because of structural factors. The "20%" figure one sees bandied around was prior to ROSLA and Circular 10/65, so O Levels were only being taken by those that passed the 11+ and voluntarily stayed on to 16, who were disproportionately boys. Just as the increase in university takeup in the 90s reflected as much as anything else the admission of the previously missing women, O Level pass rates increased because more people were being entered for them.
An increase from around 40% to 60% over thirty years when, for example, the incidence of university education amongst children's parents will have gone from 2% to 30%, the qualifications of school teachers will have increased beyond recognition and vastly more money is being spent on education doesn't seem, of itself, surprising.
I forget the exact figure, but I think in 1918 something like 2% of children got school certificate. Rather as with university admission, most people appear to think the year they did it the qualifications were worth something, but it's all been downhill since then.