Would it matter where to study your degree at?

I am a student who has a strong interest in studying medicine. I have asked several people to answer my above question but nobody was able to. Would it really matter whether you study at University of Leicester or University of Cambridge? I want to study at Leicester because it is a local university but its standards are not higher than Cambridge or Imperial College London but would the qualification be the same when graduating? Would I have about the equal knowledge and opportunities when going for my specialization? Or do all these factors depend on the student self?