Private adult assessment and costs?

I'm considering getting an adult autism assessment. I'm in my mid 30s but it's something I've been thinking about for a long time. My older sister was diagnosed in her 20s and has been encouraging me to do it ever since but I've always found the process intimidating.

The reason I want to do it now is because I had a baby earlier this year and I think it would be easier for him if I have a diagnosis, should he turn out to be neurodiverse.

My husband also has siblings, neices, nephews etc who have been diagnosed with ASD and ADHD so there's a reasonable chance.

I can't face the wait on the NHS, as it makes me too anxious, so I want to go private.

Has anyone done this, how long did it take and what sort of cost was it? I've done a little.bit of research and there isn't much transparency around costs.

Thanks

EDIT / UPDATE

Thank you for all of the suggestions. I decided to go with the Adult Autism Practice https://www.adultautism.ie/.

There was a bit of a wait (3 months) but it has been a very positive experience so far.

I paid €850 which came to just under £775 with the current exchange rate.

They've also suggested I look into whether I might also have ADHD although they don't specifically assess for that.