If you are on a monthly contract, as opposed to a pre paid agreement, then you will probably have to pay a contract termination fee to get out of it, unless they have broken the terms of the contract in some way.
Do a bit of research and find out just what their rivals are offering new customers, as it may well turn out that you are jumping from the frying pan into the fire, and paying for the privilege.
It is important if you are changing mobile networks, or getting services such as 3G or mobile broadband, to check that you can get reasonable reception for the service you are considering in your area. You dont want to be paying money for something that you cant use in your area. You can check this by doing an online location search, although these are calculated using mathematical models, rather than real world measurements, so you might want to ask some friends who live nearby what their experiences with a certain provider have been like.
Once you have made up your mind what service provider you are going for, it is time to let your existing provider know. You will need to ask for either a MAC number, if it is your broadband connection you are changing, or a PAC code if you are changing mobile network.
If you want to keep your old phone number when you move to a new network, then you will need the PAC number, but if you are happy to take on a new number then there is no need. You cannot, however, switch broadband providers at all without a MAC code, so make sure that you get it.
Thankfully, broadband providers have to, by law, furnish you with this number within five days of the request. If they use delaying tactics, you should threaten to complain to Ofcom about it, as this usually speeds things up.
Once you have given your code to your new provider, the switchover should take no more than two days. If your old provider fails to authorise the switch within this time, then you should complain to Ofcom, or at least threaten to.