London uni insurance accommodation

I’ve firmed Cambridge and insured LSE
I don’t think im going to meet my Cambridge offer but there is a chance I might (if the gbs are low enough 😭)
I’m really confused about the accommodation situation
Since I insured lse I don’t think I’m guaranteed accommodation with lse but I can try apply for some of the vacancies?
I’d really like a room with en suite and wouldn’t mind going private
But since I don’t know where im going for uni I can’t pay any deposits or anything and I fear all the good accommodation postings will vanish by results day
Any and all advice appreciated 😭🙏