UK author COMPANY with a US publisher
Obtain an EIN by phone.
Here is the current SS4 application form, plus instructions.
Complete a W8-BEN, send to your publisher.
It confirms that you are a UK taxpayer and will account for all tax on your royalties in the UK. Therefore they do not need to deduct US tax from your royalties at source.
Here is the current (latest issued Feb 2014) W8-BEN form –
Certificate of Foreign Status of Beneficial Owner for United States Tax Withholding and Reporting (Individuals)
and the US Internal Revenue Service (IRS) instructions on completing it.