I'm in almost the same boat as you. The Job Centre are a bunch of unhelpful dicks, I would dispute that letter if I was you. I'd consider myself very employable and adaptable and I'm still having a hard time getting a job since June. I'm due to move in with my girlfriend in July and if I don't get a job before then I'm pretty much fucking both me and her over, and having that hanging over my head isn't making it easier.
Like everyone else has said, don't let it get to you. Letting it get to you is a downward spiral of inactivity. Make sure you do something that makes you happy or feel good regularly to balance the stress out.