Hi and welcome 
There are very few absolute no's in the UK, and disabilities and health issues are all considered on a case by case basis - it's not a blanket thing, it's about how your condition affects you. The individual circumstances are really important.
A lot of adoptive parents have had previous MH issues - usually depression or anxiety. I've had depression, so have a lot of the parents on this board. Your anxiety and panic attacks will not be a total barrier. Right now they are recent, but you are thinking of adopting in a few years time, and if in a few years time you haven't had a lot of recurring panic attacks etc, it should be fine. They'll be looking at - how long ago was your anxiety/depression etc, how are you managing now, did you seek help for it at the time, is it very likely to occur again etc?
When it comes to long standing health conditions, again it's very case by case, and it's all about how your condition affects you personally, how you manage with it, what you can and can't do, and whether you can parent a child into adulthood with your condition.
I know adoptive parents with long standing health conditions, and have read the stories of others - I know an adoptive mother who needs a wheelchair full time for instance, and I read the story of an adoptive mum who has Cystic Fibrosis, who was turned down by oe agency but found another who were happy to assess her. I found this thread on fertility friends for you, I hope you'll find it reassuring 