i am planning to apply for LLM in USA university, i wonder whether my LLB degree ( University of London, external) is quaified to apply.
if i am not able to submit any letters of recommendation, would it affection my application?

if you can not provide any (???) letter of recc. that would definitely jeopardize your chances to get in....
(it means that there is no one out there that is willing to support you.... that's not a good credential...)

Come on, isn't there ANYONE that can write you a couple of letters? I'm sure there is. Yours is a prestigious university, that means you are a smart guy, therefore I believe you will find someone.