I think that the British public are better informed than most politicians make out. When the politicians don't like the way the public thinks then they say they don't know the facts and so on. I think there is a basic understanding of what the constitution would entail. Whichever side wins or loses then the other will claim that the other side has brain washed the public.
I really don't know how well informed people are...I have only talked to a few about it; it isn't easy to tell how much those who would have the motivation to vote know about it.
I agree that the Government are quite untruthful in this respect, when they disagree with the public concensus. I think referenda in the UK are somewhat limited in use for similar reasons; they aren't held unless the government's desired outcome is likely, and if it fails, then we can always have another referendum....
The reason, by the way, that I am somewhat doubtful about how informed many members of the public are about political issues, is principally because of the advertising parts of the general election campaigns. They are expensive, so I reason that they must be effective; otherwise, what would be the point? Yet they are not encouraging informed decisions; anyone voting on the basis of (most) advertising posters is, in my opinion, not making an informed vote.
~netweaver~