Well that's very silly of him.
In the first instance I think you need to talk to him and make him aware that you have seen this emails, that you are upset by them and what he feels is missing from your work that makes him think you're not doing your job well, (I know, I know... he's the one sending bad emails but you have to be professional about it and listen to his side too). Personally, if it was me, I would take either a member of HR or a trusted collegue or a unison representative in with me too. I
t could just be that a bit of mediating is needed and the situation will resolve but if this turns in to a grievance then it's best to have someone with you who can corroborate your version of events too.
When talking with him try and remain calm and neutral. As I said, the intention is to resolve the situation and move forwards. It might even be an idea to write down what you want to say so you have something to reference.