If they are IAPT then forms of therapy offered are limited.
Dynamic Interpersonal Therapy (DIT) is based on psychoanalytical therapy but is stripped down to the same timescale and it's for not depression, not anxiety.
You can cross borders of IAPT's for treatment if it means accessing services you need, the NHS Charter was updated a couple of years ago to allow this to bring parity with physical conditions (not that any of us probably knew that was the case for those either? ) but you can't select the type of treatment which remains in the hands of the assessor.