The problem with 'sovereignty' as an argument is that it starts from an assumption that the nation state is the 'natural' place for sovereignty to decide, and that any and all deviation from this is automatically wrong. Yet I don't this argument convincing.
Firstly, the UK is part of a number of an alphabet soup of international 'clubs'. We're part of the EU, but we're also part of the European Court of Justice, Interpol, the UN, the International Criminal Court, the International Atomic Energy Agency, NATO, the World Bank, the World Trade Organisation, the IMF and the OECD. And that's just off the top of my head. Each of these organisations presents some challenge to 'sovereignty', but sovereignty is not in itself the key factor in our membership or otherwise of these organisations. Membership is instead decided on cost-benefit analyses; by giving up a little sovereignty (the 'right' to pursue an aggressive, offensive nuclear weapons capability, for example) we get a reward (the ability to persuade other countries not to do likewise). Of course, with the EU we give up more sovereignty, but then the benefits are much more immediate as well. Nobody at all is prepared to argue that we haven't benefited from the single market, for example. Complete national sovereignty is a pipe dream, and the actual examples we have that come anywhere close to it - Kim's North Korea, Hoxha's Albania - suggest that it wouldn't be worth getting in any case. Shouting 'democracy' isn't enough either - the EU is more democratic than any of the other organisations listed above, even though it isn't very democratic at all. Ultimately, the discussion still comes down to a cost-benefit analysis.
Secondly, as I say, I just don't agree with the idea that legitimate sovereignty can only be found in Westminster. Arguably, there should be a level of individual 'sovereignty' as well. So if the EU protects me from the sort of bonfire of worker's rights proposed by Beecroft, for example, then that could be argued to be protecting my sovereignty. Freedom of movement, working conditions, health and safety and environmental standards - these are things the EU have improved that have improved my freedom, and those of most others. Workers rights are democratic in themselves.
Thirdly, Britain definitely has a 'democratic deficit' all of its own. In a country with first-past-the-post elections, and non-mandatory voting leading to turnouts of 65 or 70%, governments now regularly come into power with a mandate of no more than a quarter or a third of voting-age adults. The upper legislative chamber is the second largest legislative body in the world, yet contains not a single elected member. The head of state isn't elected. Furthermore, not only do the people crying 'democracy' have no interest in changing any of this, but they have no interest in other democratic reforms either, and usually the reasons for that are instructive. In America, for example, most states directly elect judges. So why don't those complaining most bitterly about democracy propose this? Probably because they've performed a mental cost-benefit analysis, and quite rightly concluded the idea has way more costs than benefits. Again, 'more democratic' is not an exact synonym for 'better'. We need to look past the buzzwords.