You need the form W-8BEN. It is available online.
Under part 2 section 9 where us asks which country you complete United Kingdom (Not UK, England etc.),
Under question 10, it is article 12(2). Later in the same question where is says explain the reason, you state "beneficial owner is resident of the United Kingdom"
*I am not a tax lawyer, but have undertaken work for US companies, and had to complete these forms.