Fingers crossed that your loan can be approved soon.
You can contact LBS first to see if they can provide any accommodation for oversea students or any useful information that can assist your search. If they don't, I suggest you come to London a bit earlier thus have more time to find an ideal place.
Regent's Park, where LBS is located, is a very central place in London. The rent around that area tends to be quite high. Here are two web sites you may find helpful,
http://www.gumtree.com/
http://www.loot.com/
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