BRT can be very, very, very good, providing a lot of mobility at a fraction of the price of LRT. Actually, BRT which is completely separate from other traffic can be a lot better than LRT running in mixed-traffic.
I doubt London could pull off true BRT, though, and the temptation to water it down would probably mean we don't get quality BRT. But what if the decision is between BRT with almost total coverage connecting many parts of the city with rapid, versus LRT down one choice corridor that will serve many fewer people? Given the relative costs, this might be the choice.
For anyone interested in learning about BRT, LRT, streetcars, and a lot more (instead of just parroting that "BRT is just buses, and buses are terrible"), I'd recommend visiting
Human Transit. The transit planner who writes the blog does a good job of explaining transit's basics, and why it's important to be technology agnostic.
London shouldn't rule out any technology. I think what we want is improved transit to offer better mobility. There are a lot of different ways to provide that- we should go through the process based on ours goals and the problems we want to solve, not preconceived notions of what we think the solutions should look like.