...there was a shot of a track worker setting up a temporary speed
restriction sign on the track somewhere on the Met. He stood astride
one of the juice rails, bent over, and put a metal frame thing right
next to the rail! ... presumably the rails were live. How close
do you have to get to the rail for there to be a danger of arcing?

Practically touching, and also practically touching a ground (earth)
at the same time.

Depending on which rail it was, the voltage is only about the same
as you have in your house, or it's twice that. And you don't worr
about electric arcs coming out of your light sockets, do you?
What's different is the current (amperage) that the power supply
is set up to deliver without tripping a breaker, which will be much,
*much* greater. So if there is an arc, it's a much bigger deal.

What if he'd stumbled or fainted?

If the rails were live and the metal frame thing managed to touch a
live rail and also a running rail or something else earthed, both
at the same time, you might have seen some fireworks. If he managed
to do it with his own body, he could have been killed -- but he was
probably wearing enough clothing to make such a double contact
practically impossible.
--
Mark Brader, Toronto | There is no step function between "safe" and "unsafe".
| -- Jeff Janes

My text in this article is in the public domain.