126 don't know how much more to say it, but no, current academic working conditions aren't a result of the cohort participation rate, but to changes in management and research funding streams.
Eg. When successive governments made research funding conditional on outputs, soon in order to get hired you needed to demonstrate you had a certain number of RAE/REF outputs. The coming of email and changes in the school teaching system meant students expected emails returned overnight, much more hand-holding, etc. Admin and report-writing increased. More of the university started to be funded by soft money grant applications, and the hurdles for applying for those got more and more extensive. New criteria for applying and accounting for research money from HEFCE were introduced that involved more additonal work outside of core business (eg. "Impact"). At the same time, relocated to the department for Business and Industry, universities were encouraged to adopt private sector cost-cutting measures, including a focus on profit, funneling money upwards to management salaries whilst holding down pay elsewhere, and the adoption of more and more fixed-term contracts, and not replacing lectureships on retirement (or sometimes replacing them with short term "teaching fellowships"). There's a lovely table doing the rounds at the moment of VCs' salaries - the top 10 VCs' salaries are now all over 356k, whilst real pay has dropped by 13% for the rank and file-ers in the last 5 years.
In my department, 15 years ago most postgrad students were home students, many of us with some kind of small research funding stipend, and most of my cohort went into HE teaching in some way. Today, research funding for HE has been so cut to the bone that a research stipend for a UK student is as rare as hens' teeth, and though the numbers of research students haven't really changed over those 15 years, now the majority of our postgrads are overseas students, either paying full fees or on studentships from their own countries (to which they return afterwards). So no, of that 40% actually fewer of the UK cohort are funnelling into working in HE, not more.