Others have responded abstractly with why this isn't a useful distinction, but I'll do you one better and give you a history lesson.

In 1649 Charles I of England was executed by order of Parliament. Parliament drew a distinction between the Crown and the person wearing it. Their loyalty was to the Crown. Having killed the King they decided to try being a republic.

Parliament is sovereign. But elected Heads of State are trouble - parliament eventually figured this out and got a new King instead.

They haven't really been subjects since the UK became a constitutional monarchy (defined as when a monarch is "a sovereign who reigns but does not rule" -- Vernon Bogdanor, ref wikipedia). So, not for the last few hundreds of years at least.

They can be subjects, nationals, and/or citizens. Those are all distinct and all still valid, and it is possible to qualify for more than one at the same time. Including those of us who don't qualify for any of them, there are 8 possibilities.

The UK has a web site that attempts to help people figure out what they are and what they could transition to. It's insanely complicated.

They are de-facto citizens, and the UK Monarchy has effectively no power, ergo your comment is moot, and deflects from a very real and tangible issue of democratic deficit in the EU.

The EU is far more democratic than the UK. In fact I happen to think that FPTP is one of the contributing factors to Brexit. For decades people have been living in areas where their votes didn't matter at all.

"The EU is far more democratic than the UK."

This is demonstrably false.

+ The UK (like other European nations) has a fairly vibrant democracy, with representatives who make legislation.

+ People know who their reps are, and vote on the basis of party ideals.

+ Governments live and die (i.e. they fall) on votes made by reps.

+ Governments are hugely responsive on many issues, and have no choice but to bend given popular demand.

+ There are popular plebiscites on major issues such as Scottish independence and Brexit.

Contrast that with the EU:

+ Nobody related to creating legislation, or providing strategic or material guidance is elected. Nobody speaking on behalf of the EU is elected.

+ MEP's cannot introduce or amend legislation.

+ Pragmatically, there are very low voter turnouts, and people have generally little knowledge as to who their MPs are, or what the platforms are.

+ There are no popular plebiscites, but worse, due to the above, the EU Executive is notoriously tone deaf to the will of the people. (They just don't care, because they think they are 'right' - which is a natural thing frankly in any body that doesn't have to worry about the status of their power)

+ The legal foundation of the EU, based on various treaties, most notably the Treaty of Lisbon, is on shaky ground. French voters literally voted against the Treaty, and it was enacted anyhow. This is not a 'trade agreement' - this is about devolution of major constitutional powers, so this is a problem. Referendums were cancelled in other nations because they would have been lost.

...

Summary: the UK, much like most other European nations, is considerably 'more democratic' than the EU.

If you're going to take a boldly contrarian stance, the onus is on you to provide the evidence.

It's funny how you only ever hear this (complete nonsense) meme applied to the UK, and never to say Canada or Australia. Even though it's the same queen...

That hasn't been true since at least 1983.