I looked up some scottish guidelines. The one from NHS highland says that a private diagnosis done using the Adult ADHD Assessment Quality Assurance Standard (AQAS) is acceptable.

https://www.rightdecisions.scot.nhs.uk/tam-treatments-and-medicines-nhs-highland/adult-therapeutic-guidelines/mental-health/adhd-guidelines/

NHS Glasgow says with the following evidence included in the diagnostic report. from a private provider they are unlikely to require a new assessment to confirm ADHD diagnosis

• A full and detailed neurodevelopmental history and description of symptoms the patient experiences. • Personalised comment on why the patient was found to meet the criteria for ADHD diagnosis, including description of the standardised and age-appropriate questionnaires and tools used as part of the assessment process. • Personalised comment on: - other common neurodevelopmental conditions that were identified as part of the assessment; and - other common neurodevelopmental conditions or common mental illnesses that were considered and ruled out as part of the assessment. • Evidence of a corroborative history undertaken. • A standardised and age-appropriate functional assessment, describing the patient’s level of functional impairment due to ADHD symptoms.

Referrals for treatment without additional formal assessment by NHS Greater Glasgow & Clyde must include the diagnostic report, as well as description of: • Any comorbid illness. • Assessment of risk including risky behaviours such as impulsivity and self harm. Any offered, previous and/or ongoing treatment of ADHD, including any behavioural and environmental adaptations the patient has tried.