Apply now for a Masters in Econ from LSE- it’s 1 year, and applications are still open. You need a 161+ on the Quant part of the GRE. That will get you in a position to get an intro consulting job at a top MC firm. 2 years experience, and apply to whatever MBA program you like. Done and dusted: in 5 years you could have a Masters from LSE, an MBA and 2 years experience at a top MC firm and can go any direction you like.