Just graduated in Soc Anth from LSE.
Firstly, don't worry about grades. If you meet the requirements, then apply. It may be competitive, but a real desire to do the course, and that transmitted through your PS should see you fine.
When I asked a department member specifically about what s/he looks for in PS, they said a clear passion for the subject. That's, above all, what you need to convey.
Also, the course requirements are misleading. Never judge the value of a course by the grades it requires to get in. I spoke to members of the department about why LSE's requirements for Soc anth were so low given that it is considered to be 2nd best in the world for this subject (and you can't really compare it to the American stream of anthropology (cultural anth) anyway!) and the idea is that they are interested in giving a wider selection of people a chance. What you would expect from an anth department! Basically they know that sometimes people get lower grades than they wanted/expected or are perhaps not in an environment where they can achieve AAA but they may still be the best at anthropology.
Also, regarding UCL, LSE or Goldsmiths... I do not consider Goldsmiths a rival to either of these. In fact, I haven't heard it talked about as such. UCL is fine, and good for those preferring certain areas of interest, but LSE is incomparable in terms of teaching. AFter all, it was pretty much where social anthropology was created. You could put this down to my opinion, but having spent my time there, I've heard a lot about what the people who know think, and you get a sense from the readings about where is cutting edge. To my knowledge, i've not read an article or book by someone out of Goldsmiths. And only a few from UCL. Sussex is brilliant and so is SOAS. And these, for social anthropology, are much better respected than Goldsmiths (and even UCL). Of course, you may not be after 'the best degree' or 'the most respected course', and lifestyle factors should come into your decision.
Anyway... there's my two cents!