I am doing my Master's right now at the LSE and I have to tell you that I found my undergraduate thesis absolutely indispensable. What I tell people who ask is if you don't plan on going past your BA, don't bother, but if you do, it is an absolute must. Not only does it get you a great relationship with a professor who knows your work (a great source for letters of rec). Also, it is a great way to get research experience in an environment where you're not expected to really know how to do it. At LSE they give you next to no guidance (won't even read chapters or drafts). Lastly, it gives you the opportunity for publication. I am convinced one of the reasons I got into PhD programs this year is because of my thesis winning awards and getting published.
Bottom line, do it if you want to keep going with your education. The worst you have to lose is some sleep.