In whose name is the ESB acct?
From my experience -and I know other LLs have slightly different experiences- if bill in tenants name then there's no problem. You owe nothing and can have it switched to your name and, when new tenant comes, in their name.
If it's in your name then you must pay, inc. reconnection.
Having said that, a LL friend of mine who had supply in her name cut off begged and pleaded and ESB relented. Mind you, she did tell them that she'd go to another supply company if they played hardball.