Amusingly, we are also in that building...
76 Buckingham Palace Rd in case you are interested.
It's a big building, and quite new, so a decent ratio of floorspace to footprint. Squeezing in 5000 people is probably possible if you ever managed to get to 100% occupancy, but certainly not in the last week of august ;-)
They apparently have a proper roof terrace, so no tar-paper. According to a bloke I was chatting to, a gas cylinder caught fire (oops! who didn't check the connectors properly?) and then involved a potted palm tree that was nearby. As AC said above, LFB turned up mob-handed and shut down the entire neighbourhood and even a police chopper was circling overhead. Bit OTT but then that's what happens with fires in high-occupancy buildings - 'better safe than sorry' is a well-established rule.
Big boost for the local pubs and coffee shops, although we were very unfortunate. Once we saw the smoke and realised it was a proper fire rather than a short-circuit we went into The Victoria next door - but then THEIR fire alarm went off and they threw us all out. NOOOO. Fortunately we'd just got a round in, so not all was lost, but the Plumbers Arms was ridiculously packed as a result.