Hi guys,
I have got an unconditional offer for an LLM at LSE but, for personal reasons, I decided to ask for a deferral. Unfortunately, LSE replied with a rejection and, now, I am totally screwed. In their mail they indicated a form which I can fill in order to reinstate, without need of new recommendation letter, but with a new statement.

Any of you guys has experimented this before? I was wondering what's the chance to gain a new offer for the next year..

I reinstated my application this year and got admitted again.
The procedure is simply paying the reinstatement fee of BP 50 and they will use your earlier references and you will be good to go. Found it easy.