Unless my eyes deceive me, that's a LEE Challenger Mk I press first introduced 40 years ago. You can tell from the handle, and because the press opening is offset at a 30--degree angle. The later Challenger Mk II shown looks like it had a replacement pivot & arm assembly in steel instead of cast.
Today's Mk III has been redesigned as forward-facing with a new pivot and handle linkage. The Mk III is a few years old now, and LEE only offer a 3-year guarantee in the US. I think it might be time to buy a replacement press.