The main problem is that I lack confidence - and it shows badly. I am not naturally the sort of person who is good at "selling myself". I am getting more disheartened with every interview and dread the "Thank you for coming but... " phone call. Please help.
A: You've had seven interviews so you know how to "sell yourself" on paper.
You've survived since Christmas at the sharp end of teaching, which suggests classroom competence, and your supply work will have given you valuable and varied experience. What you need now is a "critical friend" to run you through a mock interview and to give you focused feedback. You should be able to find such a person in one of the schools where you work - a professional tutor, senior manager, or NQT mentor would be ideal - or you could approach your tutor or mentor from your training year.
I'm assuming that you have already read self-help manuals about interview technique. If not, do a Google search for "interview advice" and you'll find thousands of useful sources.
"Your interview showed that you lack experience" - I don't think you do; you've been teaching for nearly six months. Make a list of the skills you've acquired and the good practice you've seen and made your own. You will probably surprise yourself. It's not the length of experience you've had that counts, it's how you've used it to develop and learn.
What I suspect may be happening in interviews is that you are not making the most of what you know. Look at your list. It's a list of achievements, no matter how small they may seem. How much of what you've written there could you use in an interview to show that you're a learner, that you're positive and reflective, and that you've made good use of your time? Use it to inform your answers - draw examples from it to give extended responses.
Your professional skills will show through. That's where your confidence will come from.
Finally, look at the competition. Many of them will be trainees. No matter how good they are, you have had the hands-on experience, and you know how schools work. You have a definite edge.