ADHD: Private or NHS diagnosis?

Hello.

I (39M - ASD & dyslexia already present) am considering seeking a diagnosis for ADHD and therefore some medication to help manage my concentration levels with it.

If I pursue this through the NHS it could take a few years. In this time, i'm genuinely worried the wheels are going to fall off my wagon.

If I pursue a private diagnosis, it'll cost a bit but it'll be quicker but am I then able to have some form of medication prescribed on the NHS from this?

I'm curious to know of others' experience of a private diagnosis.

Thanks