MSc at Oxbridge from prestigious foreign uni vs. Open Uni (UK)

So, I study Psychology at Universidad Autònoma de Barcelona (UAB), Spain. In international rankings, it's typically in second place for Spain, after UB (see https://www.ub.edu/web/ub/ca/universitat/la_ub_avui/ranquings/index2.html?), so you could say it's one of Spain's most prestigious. And I am considering applying for a MSc (Experimental Psychology) at Oxford after I graduate, or the MPhil at Cambridge. My average grades are (equivalent to) 2:1; some subjects First Class.

The thing is, time wise, I currently (unfortunately) have some non-academic things going on, so I was considering transferring to an online university to allow for more flexibility (and easier subjects, which means less time studying). Spain has a couple of 'okay' options, but as I'd be changing anyway, I considered going to Open University instead. But if it negatively impacts my future application, I'd prefer to stay where I am and take less subjects/semester.

Do you guys think that going to an UK uni (although online) could somehow impact my application for Oxbridge? Do you think/know if at Oxbridge they tend to care a lot for how well-recognised a university is, or if they go more for applicants from local UK unis?