It's not super important but beneficial. Depending on where you are applying to, are we talking Oxbridge??? if not, any work experience will be useful. You can spin your UCAS write up into how politics impacts the retail industry for instance if you're working in a shop (you always get voluntary work experience in your local charity stores). In the absence of work experience, read books with a political leaning and and write about how it has influenced your own political views. Go to the Cambridge website and read one of the recommended books for 'HSPS'. I'm writing this in 33 degrees heat so it's not a thorough as it could be but there are tons of things you could do.