Yes you may be able to get osteopathic treatment on the NHS but you will need to speak to your GP about it. Osteopathy is a fairly new addition to the services provided by the NHS which means that there are relatively few Osteopaths working for the NHS compared to private practice.
If you decide to get osteopathic sessions through the NHS just be aware that you may have to wait for several weeks before your first appointment. This is fine for chronic conditions, but if you have a sudden onset of pain, you need to be seen sooner to prevent the pain becoming chronic.