You can buy sim-free phones which can usually be used on any network, usually available from independant mobile phone shops.
You don't say which network you are on, can't you just buy a phone from them? Like I am on Orange and can buy pay as you go phones from them. You don't need to use the sim that comes with the new phone, put your exisiting one in.
If you do buy one that is 'pre-programmed' for a different network, most phones can be unlocked for about a tenner, allowing you to put your sim from anotyher network provider in.