You don’t need a deed poll to change your title: you can use any title you like, so long as it doesn’t imply a position or qualification you do not hold (e.g. you cannot legally call yourself Dr., Cpl., etc.). If you want to be known as Mx, then just start doing so. I myself use Mx. as my title in a handful of places.
If you really want, you can fill out a deed poll just as you describe, and some places – especially those which don’t acknowledge Mx. as a valid title – may appreciate this extra effort. Most folks don’t mention a title on their deeds poll at all, but there’s no reason that you can’t do exactly as you describe.
In short: 1. You don’t need to, just start using Mx. 2. But if you really want to, then yes, do exactly what you describe.