Some good tips here! And, you don't have to identify as an alcoholic to stop drinking.
I gave up drinking and didn't involve my GP, though I'm sure GP's can be helpful.
I started off by reading some Quit Lit - The Sober Diaries by Clare Pooley and The Unexpected Joy of Being Sober by Catherine Gray were the first two and they really resonated with me.
I joined Club Soda Together Facebook page. Also check out their website, they run some brilliant courses, one of which is free I think.
I went to AA. Ultimately I didn't continue going (covid), but when I did go, people were incredibly helpful and friendly.
Podcasts are great too, there are lots. My favourite is 'Soberful'.
It's also helpful to think of a few things you'd like to do instead of drinking in the evenings. Box sets, drawing, join the gym, volunteer, sleep early, anything! You might not feel like doing much at first but a few weeks in you'll find energy and enthusiasm for some extra activities!
Good luck, you can absolutely stop if you want to, and have a great and happy life without wine.