I am no expert on LBS admission policies, but I suspect your GMAT is high enough (both in terms of basic admission requirements and in terms of any score improvement having only a minimal impact on your chances of being interviewed).
The most common advice from successful applicants seems to be to spend a significant amount of time on your application essays. Some people use third party agencies to assist them with this aspect, although who knows whether that is a good idea. I just asked a couple of close friends to give me their thoughts, and not to pull any punches. As someone coming from "the professions" I found it quite useful to get comments from friends working on the business side, as the recruitment approach in industry seems to differ significantly from the approach taken in the professions (in particular, "soft skills" seem to be prioritised a great deal more; as I'm sure you know, in law/accountancy/medicine etc. strong technical knowledge/ability is often the main priority).
Also, you only have one page for your CV, so you need to be quite selective about what goes in there. I found it useful to minimise the overlap between the essays and the CV, but to cross refer where necessary (particularly useful if you are struggling to keep your answers within the word count).
Are you a round 4 applicant?