This Act does not actually offer any definition of what a “referendum” is! Is it just a straw poll? Who does it bind? We are not told. There is a vague reference to a Statutory Instrument, so presumably we need one of these in order just to interpret the Act now that we know the outcome of the Referendum.
A Statutory Instrument is like a micro Act of Parliament, and it needs to be approved by both Houses to be effective. Presumably it would authorise the Government to give notice under Article 50 by means of an Order in Council at a date of the Government’s choosing. This looks like the correct procedure we should be following now, and it is a wonder that our Prime Minister and our Lord Chancellor are not actually pursuing it so we can get on with it and stop dithering.
The Referendum Act might have authorised the Government to proceed with an Order in Council without the need for a Statutory Instrument, but it did not do so, and our judges cannot second-guess the supposed intentions of Parliament. Maybe this is a poor job by the parliamentary draughtsmen, and poor preparation by the Lord Chancellor, but this is what we are stuck with. Invoking a naked Royal Prerogative sets a precedent for a future highly streamlined referendum or plebiscite followed by the Royal Prerogative which entirely bypasses Parliament, which is something to be avoided. The outcome of this Referendum was foreseeable, there was no emergency situation, and therefore use of the bare Royal Prerogative is inappropriate. An Order in Council is like a legitimate use of the Royal Prerogative authorised by Parliament, and is often used in this way. If however Parliament omitted to authorise an Order in Council, then that is just what it has done.
Personally I voted for Brexit and would not pay a penny to the EU until they start getting clean audit reports. Some negotiation is possible, but not at any price. However, we do have laws in this country and we ought to follow them! Let’s hope that in the future Brexit means a return to some correspondence between laws being enacted and laws being uniformly and fairly applied.