If you can afford to- go private and go now. Don’t wait any longer. I waited a year and I regret this now as I may never be able to have children. I’m 38. My amh is 5.4. Had two rounds of EC. First yielded 2 eggs. One fertilised. Crap blasto on ice Today yielded 4 eggs. ICSI today and hoping they all grow tomorrow.
AMH is generally an indicator of how well you're likely to respond to meds, so as it drops, that does have implications for how many eggs are likely to be retrieved during an IVF cycle. What individual clinics will say in terms of how much they see that as an issue, I can't say.
The other big thing is your age - unfortunately as we age, a large proportion of our eggs are chromosomally abnormal so the success rates do drop in older women. (Sorry, I know that sounds like in talking about you like some old crone, which you decidedly are not!)
Even privately, at your age with your AMH some clinics will refuse to treat you unless you go for donor eggs. I’d suggest Zita or a London based clinic as they tend to be better at accepting older female patients.
The NHS does have a cut off for AMH below which they won't offer treatment but private clinics are more flexible - Create clinics specialise in low AMH - be aware though that success rates for women over 42 are like 1 or 2% at most UK clinics x