Clearly less than you think. Sovereignty is a binary concept; you are sovereign, or you are not. Sovereignty designates supreme legal authority - that is, the final authority, which cannot be overruled, that ultimate arbiter. The UK always is and was sovereign, because the QiP is law. European laws only have any strength in the UK because the 1972 EC Act provides them with that strength. There's a reason constitutional lawyers pointed out for a long time that the UK could technically leave the EU unilaterally at any point by repealing the 1972 EC Act. The UK obeys EU laws because it consents to obey them, and can withdraw that consent at any time by withdrawing from the EU.
The EU is just a joint project. As an analogy: I am a free man. I want to help create and sustain a local park, but I can't do it alone. As a result, I form a partnership with other likeminded people. When we are done, we all agree to certain shared rules regarding how the park should work. At no point did this ever stop me being a free man - if I don't want to obey these rules, I just stop looking after and stop visiting the park, which I have always been free to do at any point. The fact I follow these rules has not made me unfree, because I consented to these rules for the advantages they provided.
You might be great at Australian constitutional law, I don't know, although frankly I'm unconvinced at this point. But your understanding of sovereignty in general seems fairly mediocre to me. Australia will have to follow certain rules to remain an eligible member of the TPP - will it have lost sovereignty? Canada had to pass a number of laws regulating exports bound to the EU to stay part of CETA - has Canada lost sovereignty? No, of course not.