You know, you need to go through with asking him to leave if he does drink again, and be prepared that it is likely. A boundary like that if not gone through with will not have any effect otherwise. And I was told that strongly and forcefully by a therapist who was a successfully recovered alcoholic of many decades. An alcoholic may lose everything - job, marriage, friends, home - and still go on drinking. You have no power over his drinking. Sadly. But you know that if you have been going to Al Anon.
I went to Al Anon, listened to people and ended up realising that I was not prepared to be one of the partners who learnt to live with an active alcoholic. My husband was not prepared to give up drinking his denial was so strong still. (Seriously, he even met up with me one day, after an Al Anon meeting, while I was with all the people from there, drunk - because instead of going to AA which is why I booked a babysitter, he had sat himself in a bar in London and drunk. He still doesn't see it as an issue. And yes he was aware of what I was doing and who I was with).
I had all the promises, and he was so persuasive. I set the same boundary down that you did. I suspected, but he was so charming and did control his drinking better and stay away from things that smell like beer. Just came home smelling of coconut etc instead. He said all the right things, was feeling better than ever, didn't need alcohol... he could do this, didn't need AA, would of course go straight away if he couldn't manage on his own, was strongly considering a treatment centre, even spoke to them. Anything to make me relax.
And I caught him red handed, he still lied and tried to get out of it. And did nothing to try and mitigate what was happening. Just blame me and get angry. He has now been out of our marriage for over a month, and still blames me for the separation, it was my unreasonable behaviour, not his. He is still in denial. So he is quite prepared to lose everything, the wife he said over and over again was the best thing in his life, his young children, his home, his marriage. Makes no difference. The disease is so strong. And I feel so sad for him. And I would ask him to leave again and go through with my boundary.
He did go to a Dr years ago and had liver tests, of course some damage (blood testes) and offered pills to help him stop. Didn't take. But after that was being treated privately, so not sure what the NHS offers. I think it depends on area and region. There are group therapy and courses in some areas. Good luck.