Yes, that's the bit that I find a little odd. There's a coffee stall at the end of the bridge - you can see it, and a cluster of people by it in the last picture/vid (it's on the right hand side of the bridge as you look at the pic). I don't know what time it shuts, but it's clearly open at the time he arrived at the bridge.
So how long did he spend to-ing and fro-ing there? I'm guessing he can't have jumped from the right hand side of the bridge, or surely coffee stall customers would have seen him. So left had side, and just wait until no other pedestrians?
I don't think he could have got in a car on the bridge itself - it's a very conspicuous place for a vehicle to pull over, also he's have to climb the barrier that separates pavement from road, and someone doing that would also be conspicuous and memorable to any passers by
I think he must also have been towards the north side of the bridge, as the footage on the BBC site shows that the camera that is covering the bridge from the south has a clear view of the railings (on both sides of the bridge) and a jump would have been seen, as would his zigzag between peering over railings and back to main pavement. But once over midway, that camera would lose him, and it seems he was picked up nowhere on cameras to the north side.
Hence assumption that he left the bridge by jumping (especially if the zigzags looked like practice runs)
If you want your tin foil hat on, there is one other place he could have gone - which is a small piece of scrub where the bridge meets the embankment at the northwest of the bridge. There's even a novel, whose name temporarily eludes me) where the protagonist had to hide in London and that spot was where he made his den