If you don't have the UG grades forget about it unless you specialise in something highly mathematical.
Otherwise any of those courses at the LSE or Imperial. The name of the Uni definitely matters as far as getting into an IB goes and the vast majority are oxbridge/LSE/Imperial with the rest trailing far behind.
Maybe straight Econ at the LSE if you take Capital Markets or something as your option. Although it's a lot of work learning crap that has no IB relevance as far as macro and micro go, the stats course will at least teach you some proper distribution theory.
You'll need a First to get into the LSE and probs Imperial too; if you have that why are you not apping straight to IBs? They don't give a crap about a PG degree. They also have a 1% acceptance rate into Econ and it costs like £25k.