To enter a property, a domestic services provider must have a warrant issued by a court. Without a warrant, no one can come into your house to disconnect you. The only way that they can obtain a warrant is by persuading a court you haven't made any attempt to contact them to resolve the problem. This might lead them to believe that you have moved out, and that to leave services connected to the property may endanger neighbours. This is a good reason not to ignore your problems with debt, and to always keep in contact with your creditors.
To get this warrant, there has to be a hearing for which you should receive a summons. Make sure you attend the court with your financial statement and details of the payments you have made and explain to the magistrate your debt problem. They are usually very sympathetic, so don't be nervous.
If you are unable to attend the hearing, write a letter instead, enclosing your financial statement along with an offer of payment of whatever is affordable by way of a fixed agreement. Offer to increase that payment in the coming months, as and when your circumstances improve as a means of clearing the arrears. It is likely a magistrate will accept your offer, rather than go to the expense of rescheduling the hearing. However, if you attend court in person it will improve your chances of a settlement that you will find manageable.