Sorry
@Officer Dibble, I didn't answer this when you asked earlier because I figured it couldn't be him if he'd been seen turning right out of the tube station.
The CCTV grab I posted earlier is on Bow Road, about 150m to the west (left) of the tube station. This is it on google streetview:
Google Maps
('My' man is in almost exactly the same spot as the cyclist on streetview.)
I'm minded to discount it now we know he didn't go that way, tbh, and equally I can't see that he'd be likely to end up on Wellington Way or in Tower Hamlets Cemetery Park, both of which would also require turning left.
If I retrace his footsteps on streetview as if turning right out of the tube station, the first thing I see is the newsagent's kiosk. In his shoes, with the area looking so unpromising, I think I would stick my head in and ask where the nearest toilet was, and I'm pretty sure the answer would be the magistrates' court a couple of yards further along (or perhaps he would have seen that without asking at the kiosk). If he was feeling so ill he was panicking, that might also be somewhere he'd expect to find help, probably even a first aider. So that would be my best guess of where he went initially. You would run into all sorts at the magistrates' court though, and that might have dictated what happened next.
Would there be CCTV in a court building? Streetview doesn't seem to show cameras on the exterior, which is a bit of a surprise tbh:
Google Maps