Market segmentation applies.

At the moment, if you want to sell a product to the 'west', depending precisely what industry you're in, you need (a) CE marking for the EU AND (b) UL or similar approval for the US. That's two sets of certifications, which can share some but not all lab reports. There are then sub-modifications required for the UK: left-hand-drive cars, BS1363 plugs, etc.

If the UK starts to deviate from that such that CE marking is no longer sufficient, then we're likely to see either manufacturers not bothering or just passing the extra compliance costs on to the customer.

This is before you get onto the question of trade in services, such as the UK's major financial services industry.

(I'd argue that the big undemocratic TPP, TTIP, and WTO agreements are more of a sovereignty impairment than the EU, but that's not a view with much traction)

Given that sovereignty is fairly synonymous with control, it seems difficult to argue that giving up control is not a loss of sovereignty.

... Texas has more sovereignty than the UK, because they are democraticly part of a larger union and get to choose the president of the USA.

... Scotland would lose sovereignty by becoming independent and no longer being represented in British Parliament ...

... Singapore lost sovereignty by leaving the Federation...

... and New Zealand should become a state of Australia in order to gain more sovereignty....

That makes no sense. Sovereignty means supreme power ie. being able to make whatever laws they want (regardless of the consequences or benefits of doing so).

For example the tiny landlocked state of Lesotho is dirt poor but more sovereign than the South African provinces it borders on. It can make foreign policy, they can't.

"Freedom" to act is not a state of nature. Others can inhibit your freedom unless you convince them not to, either through agreement or force.

If you don't think that the EU is a power-sharing agreement that the UK has now voted to withdraw from, what do you think it is?

No, that makes a lot of sense and accords with most people's intuitive understanding of the word. The trouble is, as you say:

If you are wholly unwilling to enter into agreements with other people then you will find it very difficult to achieve anything at all

And economic 'independence' is a real problem if you want to have a non-agrarian society. You need to import oil, electronics, pharmaceuticals. This is what goes wrong in places like Venezuela and Greece when supplies of hard currency start running low.

What exactly is your definition of sovereignty?

Am I correct in assuming you are a supporter of the TTIP because you belive it will somehow increase the sovereignty of the EU?

pjc50's sibling comment says that maximising sovereignty by declaring one's personal independence accords with most people's intuitive understanding of the word, but I really think that can only be at the most basic level of analysis - a moment's additional thought leads you to how you interact with others, and whether they might, for example (and to be not unhistorically hyperbolic) enslave you.

Sovereignty is about being able to make decisions, and in practice (which is all that really matters) that requires deciding which other people you are going to interact with, and how, in order to get along in the world.

As to your final question, I don't have a good answer. My instinct is to be against TTIP, largely because of the people negotiating it - I imagine it will increase their sovereignty quite a lot, but probably not mine ;-).

My friend, 52% of Britain agreed with you and voted to leave the EU !!!

I'm not sure, however, that a discussion of rights and liberty is completely absent, it is just that our rights are very complicated, because we enter into a great number of very complicated agreements (which allow us, as individuals, to act with a great degree of freedom, historically speaking). Therefore, discussing, for example, the impact of EU regulation, is a discussion of individual rights, and liberty - it is a discussion about what you are and are not allowed to do, within the framework of the agreements you have signed up to.