I think that it has to do with the fact that we not only have to focus on getting the words out but also the words themselves, the grammar, etc. There's simply put too many things to focus on and since our focus is a limited resource, we divert the focus that is usually on our stuttering to the language. We 'forget' to stutter, in other words. ​ It could also be that you are role-playing when speaking English. Some people with a stutter don't stutter when they are acting. ​ For me, though, I am perfectly capable of stuttering heavily when speaking English. Or at least that was the case when my stutter was noticeable.