Article 4 of the UK/USA double taxation agreement, refers to residence. Article 7 of the UK/USA double taxation agreement, refers to business profits.
Paragraph 1 advises that the business proftis of an enterprise in the UK, are taxable only in the UK, unless you have a permanent establishment in the USA.
As the form 'W-8BEN' is a form belonging to the IRS, I regret that we are unable to advise how it should be completed.
UK/USA DOUBLE TAXATION CONVENTION