I have no doubt HM reads her red boxes.
Her boxes contain all that the government wants her to read. They do not contain every piece of legislation is full, but will contain summaries of the key provisions.
In addition to legislation, the boxes also contain briefing materials on various aspects of government: from financial matters, social policy, hiomeland security matters, foreign affairs, defence and security etc etc.
With all respect. The list with Acts, Decrees, Orders in Council, Statutory Rules and Statutory Instruments is endless, endless and endless. I am sure that neither King Edward nor his niece Queen Elizabeth read any of these documents and (did) trust completely on the competence of the departments that all what is laid in the red boxes can be provided the Royal Assent indeed.
I have taken the effort to look it up for you. On April 23rd this year the current Queen, a niece of Edward VIII, signed the following (just an outtake):
An Act to make provision about improved access to finance for businesses and individuals;
An Act to make provision about regulatory provisions relating to business and certain voluntary and community bodies;
An Act to make provision about the exercise of procurement functions by certain public authorities;
An Act to make provision for the creation of a Pubs Code and Adjudicator for the regulation of dealings by pub-owning businesses with their tied pub tenants;
An Act to make provision about the regulation of the provision of childcare;
An Act to make provision about information relating to the evaluation of education;
An Act to make provision about the regulation of companies;
An Act to make provision about company filing requirements;
An Act to make provision about the disqualification from appointments relating to companies;
An Act to make provision about insolvency;
An Act to make provision about the law relating to employment; and for connected purposes.
You really, really believe that Her Majesty has read one page of any of these Acts? Dream on. It is also physically impossible because she simply would run out of time when she would really read all of these documents.