The most common bills you will incur are as follows:
Gas
Not all properties will have a gas supply, some rely solely on electricity, but the majority will. When you move into your property you will want to check your gas meter reading so that you can confirm with your supplier that the balance was fully paid before you moved in. If you do not know who is supplying the gas then you either need to contact your landlord.
Otherwise you can find out who your gas supplier is by ringing the Transco meter helpline on 0870 608 1524.