The "British Society for Psychical Research" does not and never has existed. That name is a misuse of the name of the Society for Psychical Research (SPR) that was founded in England in 1882. Some authors have affixed the descriptor British to the beginning of the Society's name to distinguish it from the American Society for Psychical Research.
Links to sites that have referred to this organization, IN ERROR, as the British Society for Psychical Research:
http://www.occultopedia.com/b/bspr.htm