I'm surprised this article doesn't try to address the reasons this is happening. It mentions that the employers (universities) benefit from students funding themselves, and I'm not super familiar with the UK's academic system, but this seems to be an oversight by the author/editor since most PhD students (in the US, at least) are funded to do their research.
I think the most important reasons we have a glut of PhDs who can't find academic jobs are that
1. Education is becoming more universally accessible and overall education is increasing. This causes a larger proportion of the population to be interested in getting PhDs and also to be qualified (academically) to do so. Similarly, to stand out in the job market, some people may be getting PhDs to differentiate themselves from people with masters/bachelors (or equivalents), since there are so many people with these degrees now.
2. A university spends less money on salaries by having a small number of professors with huge labs and armies of PhDs rather than a larger number of professors: a graduate student will work for 10-25% of a professor's salary, and without tenure. Maintaining this ratio requires having many more graduate students than professors, but doesn't give those graduate students anywhere to go when they graduate.
3. PhD programs are often used an immigration tool rather than as preparation for academia. Many PhD students I worked with were getting PhDs so that they could emigrate from India/Pakistan/China to the US and get a well-paying job. I'm sure a similar phenomenon occurs in the UK.
4. Research spending hasn't caught up with the increasing number of PhDs.
5. Because of the research boom in the post world-war period (this occurred in the US as well), most people getting academic jobs around then were around the same age. Many of these people haven't retired yet, and they may subconsciously have introduced a new part of academic culture: you need to be old before you get a professorship.
6. Many students graduate with PhDs but without having done significant enough research to merit continuing in academia. This could have a variety of causes: publish or perish, admitting unqualified/unmotivated candidates, the academic "low-hanging fruit" getting harder to research with time.