If permission has not been given, or has been withheld, then the case should not be discussed with another party.
This holds whether a patient is seen privately or on the NHS.
However, if there is a significant risk of harm, confidentiality can be breached, but the professional would have to be able to justify that breach.
This is particularly the case where a sufferer might be so disturbed that they present a danger to their own health and safety or that of others.
In such situations, the psychiatrist would need to involve other parties, as there is a duty of care towards those who might be in harms way.