You want to make sure that the supply companies will know that you are the new owner of the property and to send future bills to you. So, sign up in advance with the companies you choose.
You need to make sure that the sellers arrange for the meters to be ‘read’ for the completion date, so that the sellers pay the bill up to that date, and you get bills only from the completion date. (If you’re selling, you need to do the same on your own property.)
There is an easy way to notify utility companies, the council and others about your change of address. You can do it on iammoving.com. You can start building your list of people to notify before completion. It will save you a lot of time and trouble.
You should have gas and electrical systems checked regularly, and you should have the first check carried out shortly after you move in. The gas boiler and any gas heaters should be a particular priority (with checks carried out by British Gas or a CORGI approved engineer).
You may want to get your telephone number transferred to the new property. You would need to line that up between exchange of contracts and completion. You should also make sure that the necessary telephone connection exists at the new property, especially for broadband.