Many universities that I've looked at have written their stance on work experience on their website beside entry requirements. Although it can often benefit you, for many courses it is not a necessity. If you can't get work experience before your university application, see if there is any extra curricular activity that might back you up, for example, a prefect role if you are in sixth form. Some schools and colleges also offer small business qualifications.
In short, I don't think it is completely necessary, but you should definitely look into having some related activities to back up your interest in your personal statement.