Firstly, you need a letter saying that you are indeed an author. I got mine from Smashwords, presumably I could have got one from Amazon as well. I contacted Smashwords and they were really good. I got my letter very quickly. It came in a very smart envelope with a beautiful stamp on it - you'll be wondering why I bothered to say that, but it is relevant, believe me.
You have to fill out a W-7 form. In the first part you tick 'a' and for additional information you put the Treaty Country as United Kingdom and the Article is 12. This will save you hours of trying to find which Article it is! Then you fill out name and addresses etc as you would expect. Don't forget to swap the day and month round in dates (probably teaching granny to suck eggs here but the American do it differently to us). Your foreign tax ID number is what we call our National Insurance Number which usually starts with 2 letters, then numbers, then letter(s).
Now for the exciting bit - there are 2 ways for a citizen of the United Kingdom to get their ITIN. The first is to send off the form, letter, in my case, from Smashwords, and your passports to the States and you should have it back within 8 - 10 weeks. OK, I can here you gasping in horror! The second way is to go to the IRS office at the American Embassy in Grosvenor Square, London for them to take a certified copy of your passport. You don't need an appointment. It's very easy. I was in and out in 10 minutes and they were really helpful. When you get there, don't have a heart attack - you don't have to join the huge queue waiting outside. Go to the front and say you want the IRS office. You'll get in very quickly.
BUT, and this is why I'm writing this, I handed over the paperwork and the lady asked, 'Do you have the envelope the letter came in?' Much to her amusement I told her that I had kept it because it had a lovely stamp. Apparently there are a lot of fakes of the letters from, I don't know if it's only Smashwords or all publishers. She asked if I had anything else about my book and all I had was a home-made flyer which she kept. She said hopefully I would get my ITIN - I should know in 6 - 8 weeks, maybe longer because of Christmas - but she couldn't guarantee it and I might have to go through it all again.
My advice: take every piece of paper you have about your masterpiece, print out royalty reports, any emails, etc, but, above all, take the envelope, regardless of the stamp!
When I hear, I will post another blog, telling you about the next stage in the adventures of obtaining an ITIN!