I mean that you have to filter aggressively, push your way through blind spots between stationary buses and cars overtaking them and all at speed relative to the stationary traffic
I disagree actually.
I just ride along until I get to a junction where lane changes are needed. If I have to change lanes, I stick my arm right out and look over my shoulder, making eye contact. This gets you let out, almost always. Whilst going through the junctions I take my position in the middle of the lane and speed up if necessary, then get out of the way again afterwards. I never ever squeeze between moving cars let alone busses, because I don't want to DIE, and it doesn't hinder my progress. Well, not unreasonably anyway.
If traffic is slow moving, then I move slowly with it. If it's stationary or almost, and ONLY then, I filter. If it looks like starting to move off again, I tuck in behind a car before the moving bit gets to me.
I don't believe that's dangerous. There are just a few hairy junctions, like Parliament Square heading towards the bridge where a load of traffic from the square wants to cut left across four lanes to go down Victoria embankment, and traffic from Birdcage Walk wants to cut right across four lanes to go over the bridge.
You either need to keep up with the traffic and watch your back, or just push/trundle along the pavement.