Request for advice (UK ND folk)

I've just finally sent a message to my GP requesting a referral to Psychiatry UK for an ADHD assessment, after intending to do so for, oh, 3 years?

That leaves my autism assessment. I've been advised against pursuing autism diagnosis through the NHS as their waiting times are like 5 years long. Do any of you have any suggestions about how I go about this alongside the ADHD referral? Should I ask Psychiatry UK to assess me for both, or am I better off paying for a separate autism assessment privately? If the latter, do you have any recommendations where I should go?