I think that King's disclaimer gives us a good point to be considered: "The application deadline is 31 March 2011.
(...) Competition for places on the LLM at King's is high and all places may already be filled if you apply late in the cycle".
What is preventing you from completion in January? In my case, I have been waiting for a referee letter for a couple of weeks, but I can't wait any longer. I will probably ask for someone's else reference.
Personally, I believe that I will be submitting the application "late in the cycle", taking into account that many students have received offers already. I know some people that applied in March and managed to succeed, but it gets more difficult as time passes on (the quota of a specific country can be reached, LLMs with same credentials may have received offers already, etc).
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