For undergraduate applications made through UCAS (the Universities and Colleges Admissions Service), you can choose between 1 and 5 courses to apply for. These courses can be at different universities, or you may choose to apply for two or more different courses at the same university. You only write one personal statement, which will be sent by UCAS to the relevant tutors for all your choices.
Since your statement will be sent via UCAS to up to 5 different tutors, you need to ensure that it is appropriate for all your options, by focusing on the subject area and the skills that you have, as well as your plans for the future.