If you are applying to several different schools using one generic statement will be easily recognized and just as easily dismissed. WHY _ because you will be seen as not making an effort sell yourself to this particular school, low effort equals low interest to admissions representatives. Remember the admission committee will likely view thousands of these statements from qualified candidates and they will spot a weakness, flaw or lack of attention to the process in a heartbeat. What you don't want to do is give this committee an easy excuse to dismiss your statement and application.
Your UCAS personal statement must demonstrate: Why you would like to study your chosen subject _ What has influenced your choice of subject _ How studying your chosen course will progress your intended career _ That you are prepared for and will be able to cope with university life _ Attending university will develop you as an individual _ Your achievements in life both academic and extra_curricular _ How any work experience you have conducted has improved you as a person _ That you are a person with a range of interests