He now does not want me to drink at all, whereas I want to really try and control my drinking again, but he does not trust I can do it because of past experiences
You've already proven though that you can't control it, you've tried and failed so your DP is right, you do need to stop drinking. Binge drinking is a problem and it isn't fair on him the way you're treating him with a drink in you - he shouldn't have to walk on eggshells or spend the night anxious when you go out because he doesn't know what he'll be dealing with when you get home.
My last relationship was much like this except I was your DP and my Ex was you. He wouldn't go out too often but when he did he would get in some states, he would come home and act like a drunken arsehole - I was fed up of it. Every time it was me that was being left to deal with him not being able to handle his alcohol. The next day he would always apologise and say it won't happen again, he'll watch what he's drinking etc. He would then be able to go out and be fine once or twice after that but then it was right back to his normal ways so no, I didn't believe him when he would say he would try and control his drinking, if he could have, he would have done it after the first time! He was also a binge drinker, would have all good intentions going out of only having "one or two" but as soon as he had those he couldn't help himself but keep having more.
I told him I wouldn't stick around if he didn't stop drinking. He stopped for a couple of months, then went out, got himself in to a state, woke me up when he got in and started an argument, when I tried to walk away to leave the house, he pushed me to the ground - it was the first and only time he had ever been physical or even aggressive in any way but it was the final straw for me. Believe your partner when he tells you he is leaving if you don't stop.
As with my Ex, if you were going to change your habits with a drink in you - you would have done it after the first time you treated him badly.
You need to make a choice to either completely give up drinking or accept that your relationship is over