Hi El,
The only requirement for AA membership is a "desire to stop drinking" . It would be better if you could go in there when you are not drunk......but please do what you have to do to get there!
There are loads of meetings in London. Have a look at the website, find one that is on today and just go. Honestly, you will feel so much better than you do right now. Take take a deep breath and walk through the door. Everyone is nervous at first but you will find a room full of people who know exactly how you are feeling and they will be able to give you a solution.
Let us know how you get on.