If I were you I would try the NHS. Make an appointment with your GP (which wouldn't cost you anything) and explain about your car accident and the fact your back is bothering you. He or she may be able to refer to you to a physical therapist which you could see for free, and you never know - they might be able to help.
In my experience osteopaths and chiropracters are not covered by the NHS, but it may depend upon where you live and what problems you are having.
Good luck with everything! I hope you feel better soon,