Mancmiamian,
You are probably stuck with buying Adderall from a UK pharmacy.
I would not try to ship it and "hope it gets through customs". If you import/possess a controlled substance without the proper legal (medical) documentation, then you are importing/possessing an illegal substance. Shipping Adderall in a box unannounced would be, from a legal standpoint, more akin to sneaking in cannabis than sneaking in birth control pills. If you make an effort with HM Revenue and Customs to obtain permission, I wouldn't be surprised if you're just directed to the processes they already have in place, which they have already vetted and control, namely, using the importer(s) they have already given permission to.
In the US, three entities have to agree to prescribe more than an one-month supply: your doctor, your insurance company, and the pharmacy. I would be surprised if you ever have all three agree to give you several months' supply based on a stated reason of enabling you to ship the medication out of the country to bypass the cost of export/import controls. Unusual prescribing practices being flagged by the DEA and lack of knowledge of UK law are just two of the reasons why I think you won't get much help from America. I could be wrong here--I'm just saying that I would be surprised to be wrong here.
Having an American doctor in the UK prescribe Adderall will not get you around the issues above. Such a doctor will either simply use a DEA number to have it dispensed from an American pharmacy, or a GMC number to have it dispensed from a UK pharmacy, and all of the country-based legal/financial barriers will apply.
Your best bet is to concentrate your efforts as follows:
1) Find a doctor familiar with Adderall and its use in adult ADD/ADHD. For a doctor to be familiar with it, they need to either have experience using it (likely an expatriate doctor in the UK), or have been well-read on its use (likely an NHS consultant psychiatrist affiliated with a major teaching hospital. A start:
http://www.uhsm.nhs.uk).
2) Obtain documentation from your American doctor detailing why he/she has diagnosed you with adult ADD. This letter should be on letterhead with all possible contact information for the practice included, and if the doctor listed his/her state license number on it, that would be a bonus. The more well known (internationally) the practice, the better, so a letter from Mayo Clinic or a university-based practice would be a bonus. In the case of your illness--because of controversy that exists in the medical literature regarding the diagnosis/existence of adult ADD--this letter should also go into detail as to the criteria used by your doctor to give you this diagnosis. Also, because you will be requesting a controlled substance, this letter should be sent directly from your American doctor to your UK doctor, as a copy from your hands will be viewed as having the potential of being altered.
You are seeking a controlled substance with abuse potential for a diagnosis that many practitioners either believe doesn't really exist or cannot be reliably diagnosed. Many entities on either side of the pond will think of how to limit their professional risk in helping you, so you're going to need to have a lot of patience and play by the rules to maximize your chances of receiving help while you're in the UK. Keeping this in mind when you deal with people regarding your situation will serve you well. Good luck.