Dude, booking into a private clinic for a test is not going to solve the situation. Admitting the problem is the first (and hardest) step. If you don't seek help now and apply for your licence, there is a (small) chance you might get your licence back. Without addressing your issues, this is the WORST thing that could happen. At best, you might carry on for a while and maybe get caught DD again, at worst you might kill somebody.....thinking of telling the truth and waiting another 12 months. Although im thinking of booking into a private clinic to get a test done first. I dont know what to do really. My conscience is playing havoc with me which is normally not a good sign.
Cancel your medical and get some help. Try AA, try CBT, try anything - but don't try to get your licence back. I promise you, if you get the booze sorted, you will be a better person for it. I know it's not easy but it is a necessity.
Get your GP's help, get them to refer you to whatever they can. Get them to record your date of last drink and ask for regular LFT tests. This will help in the long run with your application. The GP is one of the best tools in helping people get their licence back, hopefully they may help you get your life back also.
People here are not going to judge you, they will try to help you. We have all got a back story regarding booze, some are quite scary stories, coming to this forum is a great starting point and having that niggling conscience shows that you are not just playing a game, you appear to be genuine.
I really wish you the best!