Yes. Sim cards are used by phones to provide your service so simply put you could replace the existing sim card in your phone with your new sim card. In many cases you can just put the new sim card in the phone and it will begin working, however, in some cases your phone will be locked to the network which you were previously using the phone with. This should not provide any problem as it is possible to “unlock” your phone from the current network to use your chosen network. Networks don’t like to disclose the ease with which you can unlock your phone as obviously it will lose them a customer so often there is a lack of information forthcoming from the mobile phone networks.

Do not be concerned about unlocking your phone. It is not illegal to unlock a phone from its current mobile phone network in the UK. However, if the phone has been barred by the network you should not unlock it. Typically a phone will only be barred if it has been registered as stolen, etc so in the vast majority of cases you are free to unlock your phone if need be. If you need to have your phone unlocked you could try <here> for further details on what to do.