If you want to study astrophysics at the PhD level, you should be doing it for the reason that you enjoy astrophysical research, not for the job prospects. Frankly, outside of academia and national laboratories, there isn't much demand for people with a doctorate in astrophysics. Consequently, you shouldn't be selecting an institution based on prestige but based on the kind of research that they do. More specifically, the fact that there are experts there who study things that you are highly passionate about. That way, you'll be passionate about your work and do the best research that you can.
When you make it to the next phase of your academic career, you will be assessed on the quality of research that you have performed as a PhD student. The prestige or perceived prestige of the institution is largely irrelevant when compared to your actual contributions to science.
Institutional name brands will have more of an effect if you decide to work in industry after getting your PhD, but if your goal is to work in industry, I would argue that you shouldn't be getting a PhD in astrophysics, but rather in something related to the industry that you would like to eventually work in.
My apologies if you know this already. I'm not trying to be condescending, but I figured that it might be useful to to make these points.
I should warn you that although I now study a different branch of physics, I used to be heavily involved in astrophysics research (before switching to my current subfield). So, my recommendations may be somewhat out of date. In addition to the top three schools that you mentioned, I would also throw in Cambridge's Institute of Astronomy of being a generally great department as well as Manchester, specifically for their pulsar research.
However, although these departments are good overall, they are of no use to you if they don't have people who are interested in the same things your are interested in. My suggestion is to for you to talk to your current lecturers who are astrophysicists and ask them where they think the interesting research is coming from for your particular topic of interest. This should start to give you an idea of schools worth applying to. Another suggestion is to keep an eye on the arXiv and take note which institutions are producing the papers that you find particularly fascinating. This too should provide a hint of which schools deserve further attention.