CAN TENANTS LEAVE WITHOUT PAYING UTILITY BILLS?

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You are not legally responsible for any bills incurred by your tenants even if the disappear without paying them. As long as you have a signed tenancy agreement, and read the meters when they moved in , the responsibility lies with them, not you.
Utility companies are great at tracking down non-payers so don't worry about it .
In future, when someone moves into the property be pro-active and send letters to all the utility companies, Council Tax Offices etc. giving readings where appropriate and let them know that the property is let to such and such a person and that all bills are to be sent to them.

Even if they don't actually register with a utility company, and some people don't, as long as you have a signed tenancy agreement which you can copy and send to the utility company, they'll track them down and make them pay !!!