What I did was just looked through a bunch, found one that fit my needs with the shortest waiting time that I felt was okay to deal with.

One thing to note though is that waiting time only starts when they respond to you. It took like 6 months for then to acknowledge my referral for my 6 month (or whatever it is) waiting time to start. I've never seen any state how long it takes for then to process referrals, so that one is hard to guage.

I went with ADHD 360 if that's worth anything. But also I've not seen them yet either so ultimately don't now if they were the right choice yet.

Things to look for is like if you're wanting medication, make sure that they do prescriptions. If you want counselling, make sure they do that. And also look into any costs that may incur for any of those beyond assessment and that you can afford them.

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.

I've gone through problemshared recently because

• it's what my employer's health insurance offers, so I didn't have to pay
• it's only so the friction was minimal

The process was super smooth and from first GP appointment to diagnosis it was about 2 months. I am pretty sure they are in the right to choose list because my partner has mentioned this before.