I studied constitutional law

at university. There were both compulsory and elective subjects in my law degree and the two units of constitutional law were compulsory. 
I didn't find law "exciting" or even particularly "interesting". It didn't fire my imagination. I did it because I needed the knowledge for my day job...and yes, it has been useful. I have never sought admission to the ranks of the legal profession but I haven't forgotten what I needed to know - and a little more besides.
Constitutional law is the cornerstone of democracy. It overrides parliament and the government of the day. Here Downunder we have an actual document which lays out the constitution. It can only be changed by a referendum in which a majority of people in a majority of the states agree to the change. We also have compulsory attendance at the ballot box - usually referred to as "compulsory voting" - which means that most people actually vote. It is, rightly, a high bar to pass.
On those grounds the "Brexit" referendum in the UK would have failed. It passed narrowly simply because many people, often young people who supported remaining in the EU, didn't bother to vote. Unlike our referenda that referendum was not binding but "advisory". It did not give the government of the day the right to trigger Article 50 without going to the parliament. 
The media which have complained about this are either very poorly advised - or perhaps failed to seek advice at all - or they are stirring up trouble for their own ends. Suggesting that the judiciary is somehow not "independent" or "corrupt" or "ignoring the will of the people" is nonsense.  The judiciary was simply applying a major, perhaps the most major, legal principle - that parliament is sovereign. Parliament is the people - although we often doubt that. The final decision in this matter has to rest with parliament - not the government of the day. The judgment will be appealed but I expect the decision to be upheld. If it isn't then there is the potential for a major constitutional crisis.
The monarch in such a democracy, in this case the Queen, can't interfere in the governing of the country but does have the right to be "consulted" to "encourage or advise" and to "warn". My constitutional law professor, no monarchist, made no secret of the fact that he thought highly of Queen Elizabeth's knowledge of constitutional law. He referred to her as "one of the best constitutional lawyers around" but I am sure she would prefer not to deal with a constitutional crisis.
So perhaps the media needs to consult, get some advice and heed the warnings they have undoubtedly been given.