I'll start with something an acquaintance told me a long time ago; it's anecdotal, but indicative. He said (paraphrasing):
People go to college in order to be employees. People who want to be the
boss go to work.
This reflects a prominent attitude in conservative culture, that the proper purpose of higher education is to train people with professional skills that will increase the wage they draw when they are employed by someone else. Education does not confer ownership or property rights, and people who want to own and run a business do not need it, particularly. One can hire an accountant, a lawyer, or a management specialist if one likes; one does not need to know those skills to be a success. And becoming a success — in the social, economic, material sense of the word — is key to the conservative mindset. It is arguably why conservatives are so resistant to social change. They became successes within the rules of society as it is; critiquing, attacking, or delegitimizing the social order critiques, attacks, and delegitimizes their own success.
As a result, conservatives don't see much point in extended collegiate study. They might want to go a to a good university — because a degree from someplace like Harvard, Yale, Stanford, Johns Hopkins, UCLA, or etc is a mark of social success regardless of whether or not one learns anything — but that's about the extent of it. Relatively few conservatives set their eye on a professional career as a teaching professor, because even the highest-ranking professor is merely an employee of some university. One does not make real success (social or economic) in the halls of academia.
On the other hand, the liberal mindset lends itself to critiques of society. It is more interested in abstract ideals like justice or equity than concrete ideals like success, less inclined to accept the status quo as intrinsically good, and — among intellectuals, at least — curious about the structures, systems, and potential solutions that can only be found through research. Where conservatives follow their natural inclinations out of the university environment into the practical world, liberals follow their own inclinations into that deeply intellectual world that can only be found in higher education.
The outcome is a pronounced imbalance. We will naturally find more liberal-minded people in academic positions — particularly within those fields that conservatives think are 'useless' — just as we will naturally find more conservative-minded people among business owners and CEOs. I'm sure the same is true of the UK civil service. It's a feature of the system, not a bug. There's no way it could really be otherwise, short of a whole lot of conservatives abandoning the things they value to fill academic positions in fields they consider useless.