>* Even the current UK government doesn't try to argue that the UK has lost its sovereignty by virtue of its EU membership. Its own white paper on Brexit acknowledged that the UK was still entirely sovereign.*
It's not something that's dependent on being acknowledged though. If your national laws have to comply with the laws (or directives if you prefer) passed by a third body, you concede your sovereignty. That's explicit in the very notion of sovereignty -- no matter how politicians might spin it.
>but my position on the sovereignty argument is that for me as a UK citizen, it just doesn't matter since I have such a minuscule say in how things are run either way.
That's a justifiable position one can legitimately hold.
But others can also legitimately feel that it very much matters. And historically and morally, the issue of sovereignty of a national state was never a light one to be set aside with "who cares, we don't very much affect our national policy anyway".
At best it's a stance that's ok for times of plenty or favorable laws, but that starts to matter more when the decisions that are taken go against a countries interests -- and there is no way to overrule them in the national level because even though e.g. 90% of the British are against, 60% of EU policy makers want them.
And despite the talk now being of right wingers being in favor of Brexit, we can very much imagine the opposite: a right wing EU (with e.g. Marie Lepen, the Netherlands guy, some German equivalent etc) that imposes right wing directives and laws upon a progressive Britain. (In fact we don't have to look that far for that: the EU has long impose right leaning labour laws upon more left leaning states).