As a non-native English speaker I stutter mostly when I am talking in English. Any tips or suggestions to improve fluency and not stutter?

As a non-native English speaker I stutter mostly when I am talking in English. Any tips or suggestions to improve fluency and not stutter? Hi there, I am from Bangladesh and my native language is Bengali. I have a mild stutter and some minor lack of fluency in Bengali. There are some sound blocks, repetition, lots of filler words, repetition of phrases and so on. My voice is also cracky and the melody is not there. I don't know all the terminology out there so I can't explain it. In one word I would say that the way I talk is much less fluent and elegant than other people. Now, I grew up in an English medium school where they taught us everything in English. Both the spoken and written instruction was in English. After my A'levels till now, the written communication is in English, but there are no spoken communication in English. So now when I try to speak in English, my stuttering becomes absolutely horrible. The slower I try to speak, the more my attention is focused on saying the words accurately and that increases the stuttering. Sometimes, when I am talking fast without thinking, I sound a bit more fluent. I am also unable to express myself as much as I want to. Sure, I understand I can never be like native speakers, but I have seen non-native English speakers to be able to speak very fluently as well. My accent is horrible as well. Its just a painful mess. Any suggestions on how to speak fluently and without stuttering in English?