like if they run off owing the supply co money, followed by supply
co refusing to supply. You don't think so?

Nope. If the tenant is the holder is registered with them for the
usage at that address, it's the tenant alone who is responsible.

If they move without paying, it actually puts *you* in a better
position, in that if they took all their £1 coins from a coin meter
with them, you would still have to pay the bill (as it's your name on
the account)

If they flit without paying their bill with the electric co. you can
simply give them any forwarding address you may have and let them
worry about retrieving the costs.