Frankly, taking the BVC at the same university where you took your LLB isn't a particularly important thing, as far as I know. Given that neither Oxford nor Cambridge offer this, I wouldn't be too worked up about it.
I'm at QMUL, taking the LLB as my second degree. I know a number of people doing the 2-year programme having completed canadiam masters degrees, and they love it. QM has an outstanding mooting programme, great pro bono, a top-class teaching faculty and tutoring system, and a much stronger reputation than City (this is based on the opinions of my tutors who are also recruiters for their firms/chambers). Also, the University of London degree that you'll get from QM will be internationally recognized, and the degree from City will be much less so.
I'm the current moot master at QM, so I know a fair amount about what goes on behind the scenes in the law department. Feel free to PM me if you'd like to talk more about the university (I live near campus, so if you're planning to visit I'd be happy to talk to you about the QM experience)