When I worked in the civil service in the UK my stammer was quite severe. I applied for a job within the second and said I had a disability which got me a guaranteed interview (I got the job). I think the question on the equal opportunities page was something like, "Do you consider yourself try have a disability?" So it was up to the individual to decide. This might have changed now. I'm pretty sure it won't get you any benefits with our terrible Universal Credit and PIP systems seeing as it doesn't actually prevent you from working. You just have to figure out what work you can do.