Surely a properly democratic state should not be able to change it's constitution without reference to the people?
In which case step forward ... the UK.
In the past few years the following constitutional changes have been made or are in the process of being made (and these are just examples, there are many others):
Abolition of hereditary peers
Alternation in accession rules for our head of state
Reduction in number of MPs to 600 (currently going through)
Fixed term parliament act
Some I agree with, some I don't - that isn't the point. The point is that not one has been put to a referendum. All have been passed purely by parliament, so my only way to block them is to try to change the makeup of parliament (but I only have a vote in one of 650 constituencies) or to campaign more widely to get parliament either to take my stance or to put the constitutional change to a referendum.
And before you claim that this is still different to the EU, well you are wrong. Constitutional changes in the EU are still all subject to requirement of unanimous approval by all member states, i.e. each country has a veto. So if there is a major constitutional change in the EU my options to influence are identical to that for the UK (see above). Although I do have one further option - if I oppose an EU constitutional change and it is clear that the UK government is going to approve, I can also campaign to persuade another country to block it (e.g. Ireland) and therefore have rather more option to influence constitutional change in the EU than in the UK.