Yes, my therapy sessions are fully confidential. I am bound by the British Psychological Society’s ethical code of conduct to keep what you share with me as private and confidential.
Note that registered therapists are obliged to have a supervisor overseeing their work, to ensure they are maintaining a high level of assistance to their clients. While I might discuss the generalities of your case with my supervisor, I would not divulge your identity, and the supervisor would also be under oath to protect the privacy of any information that is shared.