I am going into my final year of the LLB at a UK university as an overseas student. I currently have a first-class overall and I am really interested in applying for an LLM at UCL and LSE. At the moment, I have one reference out of the required two. My second referee will not know me personally or be able to comment on my engagement in seminars, however, he/she will be able to comment on my academic grades.

Does LSE/UCL place significant or heavy weighting to the letters of recommendation?

Thanks in advance.