I went through Psychiatry UK for mine and they were fine, although from your link it seems they are currently one of the longer waiting lists, so I would suggest trying someone else with decent reviews. I didn’t need to wait long (maybe a week) for my referral to be confirmed, unlike the other person in this thread.
I would suggest making sure that the provider is a yes on the “Authorised to provide NHS ADHD Medication Prescriptions”. You can sign up for an NHS pre-pay certificate once you are getting regular prescriptions to save on the prescription payment.