Actually it not mattering for medicine is a bit of a myth, there are actually pretty significant differences in post-F2 destinations for some medical schools over others. but back to the topic at hand...
It doesn't really matter, as long as the course is accredited, in that where your degree comes from doesn't matter so much as what you make of your time at university. If you get involved in projects, do internships, etc. then you'll get a good job whether you're at Cambridge or London Met.
However 1) some companies do target certain universities, but this isn't as simple as them just targeting higher ranked, more prestigious, etc. unis, and those perceived lower tier universities also get targeted. And 2) the university you go to will to an extent denote what project opportunities are open to you (though it's also worth being aware that many competitions don't restrict team members to being all from a single university, so if there is another university nearby which does have those opportunities, you can still get involved, even though there will be complexities in that).