I haven't read this thread, but to answer the original question, I think that the problem isn't about whether LSE is good enough. The problem is that the firms you seem to be targetting are not recruiting very much these days (top banks, consultancies, etc). Where ever there is recruitment, the competition is extremely tough.
If you don't already have strong work experience (e.g. summer internship at Credit Suisse), I would definitely not think LSE is worth the investment, even for something like MSc Finance.
Now if you do have strong work experience already, then I think yes LSE could be worth the investment for a non-finance/economics course. Depending on the position you apply for, most places don't care TOO much about your degree, but you definitely need very good knowledge in general + very strong work experience + a lot of luck to be successful.
But put it this way: I'd say 90% of people I met during the Masters at LSE (across a very wide range of courses) left disappointed at the end in terms of employment and many (probably even >60%) are still searching 1 year later for a GOOD job.