Yes, please wherever possible, although self-referrals are accepted, the GP will need to be informed by the psychiatrist of the assessment. This is for various reasons, such as the psychiatrist often needs professional information about a child's health and development and may need to ask the other GP or another doctor to carry out further treatment.
In the UK healthcare system, the GP holds the overall view of a patient's health, and it is important that they are aware of the assessment so they can continue to support the patient appropriately.