A dictionary definition of sovereignty :
Supreme and independent power or authority in government as possessed or claimed by a state or community.
So the question is, as members of the EU, do we still have sovereignty in the UK. The answer is, yes we do. And the proof is, we are having this referendum. The other countries of the EU want the UK to stay, but if the vote is for LEAVE they won't stop us. There is even something written into the treaty called 'Article 50'. The idea that a member might want to leave is written into the EU rules.
There will be lots of discussion how this will happen, but it won't be stopped. Whether we would benefit from this is the subject of this whole website
Decisions about our lives are made at three levels. And all three levels are elected democratically. Yes, even the EU!
Different areas of policy are decided on at different levels. Most of the power liies with the Westminster government, and indeed most powers the local councils have are granted from the national government - they are kind of 'on licence'. Areas of policy where the EU makes the law are subject to treaties, like the Lisbon Treaty, and these have to be ratified by national parliaments.
But right now, less than 15% of our laws are made in the EU. The UK has a democratic say in this 15%.
As I said, all these levels are elected democratically, but the method of getting from vote to elected person differs. This is a website promoting EU membership, not electoral reform, but it is worth mentioning here that our MEPs are elected on a proportional system, Westminster on a system where full power can be obtained with less than 40% of the vote and in which the swings between governments are decided in about 200 constituencies.
The LEAVE campaign claim we don't choose the people who run the EU, but if you live in, for example, Barnsley or rural Hampshire, your vote has more effect at European level. The Sovereignty argument is about giving power to our people
But if the UK leaves the EU, that would means concentrating power at one level, and its a level where half the UK Electorate population do not have an effective choice now.