I don't want to be drawn into this debate, although its very tempting. I don't know what kind of people the OP hangs out with but in my circle of friends (BSc Econ, BSc Govt & Econ, BSc Business Maths & Stats) all of us managed to get internships last year as well as jobs this year at BBs, PEs and HFs. Seriously OP consider expanding your pool and asking around before making sweeping statements based simply on your group of friends.
LSE is totally losing its edge. The Independent League tables came out today and it's worse than Durham. I anticpate the banks will hastily cease all contact with LSE, and auto-filter anyone who applies.
Perhaps the banks are finally coming out of their little shell, and placing more emphasis on ability as opposed to institutional prestige?
Does anyone know about LSE MSc Finance placement, does it at least get you interviews?