There are 98 universities to choose from in the UK plus many colleges also offer degree courses. All the choices are listed on the official UCAS website with links to the college and university websites. As a citizen of Europe you may also attend a university in any European Union country. As a citizen of the Commonwealth you may also choose to study in any Commonwealth nation. UCAS for all UK university information and application procedures.
Application is to each individual university.
This link to the Fulbright site contains a beginners guide to applying to a U.S. university and full supporting information and scholarship information. Over the summer you may wish to visit possible university destinations to help make your mind up. Look out for the Open Days and H.E. Fairs. Select your dream course as your first choice but always make your last choice a 'failsafe' application on minimum grades in case your results plummet. The deadline for applications is 15th December and most colleges and sixthforms will aim to process your application by November latest in your second year.