QUOTE(Louise H @ May 7 2012, 05:08 PM)

Look at the local council websites in your area and find the details for the music service/instrumental lessons or similar. Not all council music services are called "x Music Service".
Also keep an eye on the jobs section of the TES website, and on www.thefms.org
In some areas, with a strong music service, much of the work in state schools will be through them. Others are much weaker, so more state schools will advertise directly. In either case, private schools will not use the music service.
How much relevant experience do you have? The application process, particularly with music services, will be looking for this. It needn't be peri work, it could be private tuition or even voluntary work with music groups. If you don't have much that you can point to, then maybe make contact with a local music service and ask if it would be possible to shadow a member of staff for a day or two: not only will this look good on paper, that you're actively improving your knowledge and expertise, but could also get a foot in the door, should you make a good impression.
Where you are in the country will also affect how much competition there is for jobs: unsurprisingly, more remote and rural music services get fewer applicants than those in big cities with music colleges and conservatoires, especially for part-time positions.