If your utilities is included on your contract, you don't need to do anything! Just show your contract upon applying the family visa. I am sure you can get the utilitiy details from your landlord. If this is required on your application, you just have to attach the contract along with it.
There's no such transfer involve, if the landlord want you to pay the utility bills, he has to close his account and you have to open it under your name and there's deposit involve!