This one depends on the cause. Some headaches can be caused by injuries or tension in the neck and jaw, this could absolutely be helped by an osteopath, chiropractor, massage therapist or TCM practitioner. Some headaches are caused by potentially less treatable things, like migraine, which your GP will more equipped to deal with. True migraine is fortunately relatively rare, with treatable causes for headache being much more common.
Good choices for treatment: Osteopathy, Massage, Acupuncture, Chiropractic, Reiki.