There is a bit of a trade-off in what subject you study and at which university you decide to study at.
You mentioned Actuarial Science so I will base my example on this course, I'm also a prospective student leaning more towards the Actuarial Science route over Mathematics.
As far as which university you attend, as far as Actuarial Science is concerned, one of the factors really worth considering is whether the Actuarial course at that institution is accredited, ie do you get exemptions from the professional exams.
The other aspect is to look at the educational experience. It is not particularly safe to say that being at a good reputable university necessarily implies that you will have a better educational experience or support there, so this is something to consider.
It is also worth noting that the university rankings are mostly, but not only, based on the research strength of that institution. Perhaps this may not be important for those who do not wish to go into research themselves at that or any other reputable university. I would say the educational/teaching aspect is what most students should consider.
I base this on two actuarial science students that I know both having gone to two different institutions studying Actuarial Science. One went to Macquire University, the other at University of Melbourne. Out of the two universities Melbourne is considered most prestigious, within Australia, over Macqurie (We have Russel Group universities here, in Australia they have a GO8 list of universities which is their Russel group equivalent, which Macqurie is not on).
The student at Macqurie achieved all his actuarial exemptions and had a good educational experience and good tutorial attention with help when he required it, Melbourne student struggled with that aspect, his grades suffered a little, and now is struggling to get actuarial jobs unlike the other who is now working as an actuary.
However, I'm only considering the grades achieved here, and by no means implying that that is the same for all students.
The other factor is, whenever I've looked at graduate work places advertised online, a lot of employers look at your UCAS points and whether you have a 2:1 minimum in your degree. So here at least, there is no indication of which university type you should have attended. Some lucrative placements may state that you have to have attended a Russel Group, but not all.
If we were to suggest that there are many graduates these days who achieve a minimum 2:1, then it is safe to say that employers place a good amount of emphasis on UCAS points for graduate entry schemes/jobs.
Indeed, usually those who have a high UCAS score is likely to have attended a reputable university, but this may not always be the case.
However, what I said here is not a blanket truth and does not apply to everyone in every situation which many of you have mentioned and/or inferred in previous posts.
I would say having a a good UCAS score, and a good educational experience which in turn could lead to a good degree is really important, but then of course your career choice and personal circumstances would determine individual university choices.