Having an extremely hard time looking for work with a stutter. Advice? What do the rest of you do?

Having an extremely hard time looking for work with a stutter. Advice? What do the rest of you do? Here in the UK unemployment is pretty bad anyway, but I find myself completely blocking when inquiring about any job. Phoning up I can't even get a hello out (obviously they just hang up), handing out CVs I can never introduce myself and ask for work. I wasn't nervous or anxious about asking and looking for work until I was rendered completely speechless in front of people. I went into my job hunt extremely positive but it's been a very long time and my inability to communicate is stopping me from even getting an interview. Stuttering effects pretty much all aspects of my life and I try to live with it. However it's now put me in a place where it's effecting the basics, food and shelter. I know I'm not going to get an interview when I hand them a CV, "refuse" to say my name, twitch a bit while choking on my words then walk away. My question is what do the rest of the stutterers here on reddit do? Did you have problems finding work? And is there any advice you could give me on my situation?