This isn't a blanket cure obviously, people have SA for many different reasons and it manifests itself in various ways in different circumstances.
(Introduction is just my view of it and what I experienced)
The root of SA is not feeling good enough. Your body trigures its defence mechanism in stressful situations even when there is no immediate danger. Your hyper aware of everyone and everything around you when there is no need to be, almost like your about to be attacked by something or someone. SA isn't rooted in conscious thought processes, its an unconscious reaction. Otherwise you could just decide not to have it which is obviously not an option. As with all mental health issues it is misunderstood and stigmatised, but IT ISN'T WHO YOU ARE, it's an infliction/disease. SA affects how you walk, your body language , eye-contact , social skills, mental wellbeing, self-esteem and confidence etc. Its based on beliefs (at least for me) that your not good enough in any area of your life and this is false. These negative doubts and thoughts have been embedded in your subconscious and this can occur through a number of events bullying/traumatic childhood etc.
I have had it worse than you could know, limited my potential for years, but I was able to get over it using this. It's a bit complicated as is mental health itself, but SA needs to be treated as a physical affliction just like any other physical ailment (and not with meds). Neurotransmitters and hormones are responsible for most everything we do, these are the reasons SA manifests itself physically, these operate on a subconscious level and we cannot immediately control how and when they are used. You need accept this fact, there is powerful undiscovered subconscious mind that is responsible for almost everything you do, and we are tied to this whether we like or not. But as humans our incredible adaptive survival tool is our consciousness, like dogs with excellent smell, hawks with their eyesight, bats with their hearing etc.
We can use our consciousness to access our subconscious mind and that is what sets us apart from every other animal on earth. When you repetitively go over something it physically rewires your brain, the neurons in certain sections strengthen and learn to fire autonomously and more rapidly. This is the case with any skill any human has learned be it driving, playing an instrument, learning a new language, playing a sport etc. These neurons can be trained without your knowing. We are only the product of our environment and genetics and had your environment had a constantly negative influence on you, your subconscious adapts to this and makes it your reality. It is unbiased as to what we feed it, for the most part it can not interpret what is good for for us and what is bad for us it simply adapts. For example Rheumatoid Arthritis and Cancer, two physical ailments that could be stopped by the brain but simply are not because they cannot be comprehended by the subconscious faculties. The same applies to SA. SA is an adaption, its rooted in social situations as they pose a threat to our survival and replication chances, embarrassing yourself in front of your peers, lowering yourself in the social hierarchy in terms of potential mates is seen as a death certificate (of course this isn't true). Your brain stimulates your adrenal glands to release the hormone adrenaline (fight or flight system) which in turn draws blood to your arms and legs readying itself for battle, your cerebrum essentially shuts down and you no longer have a conscious grip on the social situation, decision making and conversing really isn't an option when anxiety attacks trigger. This situation clearly isn't advantageous from a survival point of view when you just want to communicate or walk somewhere is it? It's exactly the opposite. But it can be fixed, the same way we learn any other skill can be used effectively to treat SA.
Positive affirmations repeated on a daily basis will change the way your brain is wired (youtube positive affirmations). Monitoring your thoughts (self-talk) for negative ones and replacing these with positive ones will allow you to develop 'confidence'( incredibly important to seed these negative thoughts out of your self-talk!!) . Constantly pay yourself compliments on a daily basis, over and over and over and in every facet you possibly can. Negative influences/people in your life that are berating you or in any way adversely affecting your confidence need to be removed. The music you listen to needs be positive. You need to avoid negative TV shows also. As I said, this is the same as learning any other skill, it takes time. You need to integrate these into your daily routine, every day. You will notice differences in monthly intervals (not daily or weekly so do not expect to)
Telling yourself your great over and over again may seem narcissistic, you may worry about other people's opinions on this behaviour. But, as with every other animal in the world, we are in competition with one another. 99% of the people around would prefer if you remained having SA, because if you get rid of it and start competing it lessens there chances of survival. This is where the emotion jealousy stems from. You become a threat. Competing would mean life and death only 300-400 years ago and as I stated before we are tied to our natural animal instincts. You can't sacrifice your potential, your future life, your wellbeing and future family's standard of living in order to allow other people have it before you.
This is a hypothesis, I am not a doctor or any other form of mental health therapist. But I had chronic SA and overcame it when I applied the above methods. Exercise and diet are essential to wellbeing also. These may or may not work for you, different circumstances apply to different people and there is no blanket cure. SA can be caused by a variety of different reasons.