British citizens don’t have to apply for a visa merely to visit the US (they do in order to work or go on business). A simple ESTA filled out online will do. There is a reciprocal arrangement between the UK and the US in which the requirement for a visa is waived for tourists who intend to stay for less than 90 days.
Actually when they go through customs in the US, they WILL SIGN a form and receive a 90 day tourist visa, my Wife is a UK citizen and when she originally came here she received a 90 day tourist visa from US Customs at LAX