Most often than not anxiety and depression are hand in hand. The best place to start is checking the NICE guidelines for recommended therapies that meet your needs. CBT is best for mild to moderate cases and for people who have one condition only and not for co-morbidities (multiple conditions, like depression, anxiety, etc).
What you describe in your questions appears to be geared to a more relational therapy, which can include Acceptance and Commitment Therapy, or even Interpersonal Psychotherapy. However, without a formal assessment of your symptoms and case history it is difficult to suggest a therapy for you. I would recommend you first book an appointment with a clinical psychologist or counselling psychologist to ass your needs.