The majority of scholarships to Britain for American students are for postgraduate study and research. There is very little provision at undergraduate level. Postgraduate scholarships are usually awarded on academic merit. They vary from nominal awards to full scholarships including payment of other costs besides fees. There is strong competition for these awards and many of them have early closing dates for applications - often as much as a year in advance of when you intend to start your studies.
Many institutions offer their own scholarships to overseas students.
You should not travel to the UK or begin a course of studies without making sure that you have enough money to pay your academic fees and living expenses. Details about the costs of studying in Britain are in the financial pages of this site. Information about scholarships for American students is available on the British Council USA web site . The British Council, registered in England as a charity no. 209131, is the United Kingdom's international network for education, culture and development services.