Does the med school you go to really not matter?

I’m in the process of weighing up my options between Imperial College London and the University of Birmingham (UoB) for medical school, (I’ll be applying this September) and I’m wondering whether the medical school you attend has a significant impact on your career, especially when it comes to research-heavy specialties like infectious diseases.
From what I understand, Imperial is renowned for its focus on research and academic excellence, with a more scientific and theory-based approach. On the other hand, UoB seems to emphasize the clinical side, with a patient-centered approach that focuses more on bedside manner and handling patients rather than research.
My concern is whether attending UoB, which doesn’t appear as research-focused, might leave me with an inferior portfolio in the long run compared to graduates from Imperial, especially if I want to pursue a career in something like internal medicine or infectious diseases, which requires a strong research foundation.

It doesn't make a difference for the stuff you've mentioned. There's plenty of ID research going on in Birmingham. Where do you actually want to go?

But wouldn’t going to London allow you to have a look at and diagnose a wider number of diseases especially for tropical diseases as London has lots of tourists, plus do you think the gap in scientific knowledge would disappear between an imperial and UoB grad during ST, as imperial is more science heavy?

My dude, Birmingham is the UK's second largest city and a major international hub for business, students etc - it's not like they have a shortage of infectious diseases or pathology of any kind there.
Just how much tropical medicine do you think you're going to see during an undergraduate medical degree in London anyway?
Use your elective to pursue niche interests like this (you could even do it abroad where you'll see much more interesting tropical medicine than what you'd get in London).
I doubt the difference between pre-clinical medicine at Birmingham vs Imperial is particularly significant. I would honestly pick the university you actually want to go to.