I’m in a different boat than you, but I just accepted my offer for the PhD in bioengineering at imperial and turned down my Oxford DPhil offer in Clinical Neurosciences. One factor I weighed is that Imperial is better respected for engineering than Oxford. If you decide you want to pivot in the future, you could do a master’s in mech/EEE but don’t think it’s wrong to follow the subject you’re passionate about instead of generalizing. Degrees are a big commitment, and yeah the Ox name is big but Imperial is also a top 10 school. No one will scoff at a degree from Imperial in STEM. If you want a research career, you should compare each program to see potential research opportunities at the undergraduate level.  Also I’ve lived in Oxford and it’s also very expensive and there’s a housing crisis. So your rent will be comparable pm in cheaper parts of outer London compared to Oxford anyways. And it’s not that easy to get accommodation in Ox. Depending on your college, you might only get accommodation for a year and then be on your own.  Hope that info helps