BPS-British Psychological Society
http://www.bps.org.uk. Like iammichealjackson says this is the organisation you would register with if you were planning to end up a clinical psychologists. Some psychologists are trained to work clinically with individuals in a therapeutic environment and are known as clinical psychologists. You typically find clinical psychologists in hospital and clinic settings. You first need a psychology degree, and then train at post graduate level. This is a very competitive career.
Psychotherapy is a little different, and can be a confusing field as there are so many models, each have their own training. You don't need a psychology degree. BACP trainings are 2 years plus and UKCP are 4 years. Once qualified you can work one to one and in other settings.
Don't worry it is a bit confusing.