Tom57 - I have some 25 years as a social worker in fostering and adoption, though am now retired and work independently assessing prospective foster carers and adoptors.
There are some helpful posts here and I agree with them. Your ME would I think pose a problem as you need a "clean bill of health" for obvious reasons. Your GP may be supportive but all prospective adoptors have to undergo a medical (with your GP) but then the results are sent to the medical advisor for the speicific l.a. to where you are applying and he/she makes a decision based on your medical history on your suitability to adopt. I don't want to say that your ME would absolutely rule you out, but I think it could be a problem.
Most children awaiting adoption are older children, sibling groups and thos with disabilities and almost without exception these children will have emotional difficulties and possibly behavioural problems because of the abuse/neglect that they suffered with their birth parents. Many people think that to take a child into your home and offer love and security is enough, but unfortunately it isn't really like that. Many of these children have been so traumatised in the past that they are unable to trust adults again adn this can lead to all kinds of difficulties. Sorry to sound so negative but I am just being honest.
Re your daughter - at aged 10 years she will of course have been used to your undivided attention I guess and she may find it very difficult to adapt to a younger child, especially if that child has behaviour problems. Adoption is a gamble and there are no guarantees. On the other hand it can be immensely rewarding and fulfilling, BUT you have to go into it with your eyes open and know about the possible pitfalls and the effect that can have on your own family. The thing is with children of your daughter's age they can't possibly conceive of some of the problems that traumatised children can bring into your home and so can never be fully prepared.
Maybe you need to think in terms of fostering to see if in fact you can cope with caring for someone else's child - you could start by applying to become respite foster carers (which means that you care for a child on specific occasions e.g one w/end per month, part of the school holidays etc) tto give the foster carers a break. There are also some schemes where you can care for a child from a family who are struggling again on a respite basis. In this way you would be "dipping your toes in the water" without getting soaking wet!!
Why not talk to your local SSD who will be able to discuss all of this with you and advise you about schemes they are running.
You could also google "British Agencies for Fostering and Adoption (BAAF)" "Fostering Networks" and "Adoption UK" - there is a wealth of info on these sites which may take yyou a little further forward SO to sum up my advice would be .............proceed with caution!
Good luck with whatever you decide.