Hi, did you complete the form at a local benefits office or did they give you a phone number? Either way, I’d contact them right away and just let them know that you realised that you didn’t sign the form and ask them what to do? Emphasise that you are very worried that you won’t receive your job seekers allowance and ask for help.
It might be a good idea to take a piece of paper with your name, address, national insurance number, date of birth and signature on it. The staff at the local office might be able to send it on with your original form so that they have your signature and can process your claim as normal.
Also, did you know that you can apply for benefits online now? You can do this at the Direct Gov website so you could e-mail them on the site to check if your application is being processed normally. If people can apply online without a physical signature, I’m sure they’ll be able to sort out your problem quickly.
Being proactive and making enquiries about your application should hopefully put your mind at ease.