I think you've made a tactical choice I'm choosing to commute, as it's financially the best option. It shouldn't affect your studies at all really, you'll just be missing out on a lot of the social stuff (which you mentioned you're not into anyway). There could be times when you stay really late to study or times when you'd need to be in quite early, sometimes meaning it would be better to stay the night rather than go back and forth. But that's really the only issue with commuting, which you may not even encounter!
However, I am also from London and felt like moving to Oxford would heighten the university experience for me. But I didn't want to pay the ridiculous halls prices in light of that. So and friend and I have a three bedroom house but we need a third flat mate to occupy the third bedroom.
Rent is £101 a week per person, which amounts to £3800 for the 38 weeks you would've spent £5000 on in halls.
If you're interested or want to find out some more
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... and the ones that won't