You can fill out FAFSA now and apply for your loans with a provisional acceptance letter. You'll have to get financing sorted before you can apply for the visa.
Depending on what your fees are, remember the exchange rate is awful right now. I borrowed $28,000 but that quickly only became 14,000 quid, almost 8,000 went to tuition. If I hadn't sold my house before I left, I'd be living in a bedsit somewhere with a view of a brick wall. Granted, London is very expensive but just consider you might need more than you think, especially if you are moving into a flat.