A lot of law graduates don't end up working at top firms. Plenty will even end up in careers not directly related to law.
Yes, top law firms are interested in the university you went to. They'll generally want you to have gone somewhere old and prestigious, and some will even like you to have done a different degree and a law conversion later on.
However, there are plenty of options for people who haven't studied at the most prestigious universities. Not everyone who studies law might want to work at a top firm. Some may prefer to work for a smaller solicitors, or work in a capacity where law knowledge is useful such as HR, or maybe teach, or even go in a totally different direction entirely.
I'm going to speculate that Imperial isn't on the list because it mostly focuses on STEM subjects, and transfers from these subjects to law at postgrad level are rarer than from the humanities.
Also, don't forget that you do have to live at and study at your chosen university for 3 (or more) years. Don't pick somewhere you aren't keen on purely because of the graduate prospects. If you're miserable, then you won't get the best grades, which are also important.