Ziemowit:
But if British Parliament had passed a law obliging every household in the UK to buy at least one newspaper a day,
-----------------------
Are you serious about that?
Yes, I am. Parliament is free to pass any bills it needs or thinks relevant. Some people will not comply with the bills passed by Parliament, so Her or His Majesty prepares fines, also prisons wait ready for them. My friends as law-abiding British subjects would certainly comply and - given the choice - would buy The Guardian. If Parliament were to force them to buy a daily copy of The Daily Mail, they would most probably refuse and would risk to be sent into prison instead.
The British sovereign is under the control of British Parliament either. If Parliament passed a bill to end the monarchy in Britain and ordered the Queen to get beheaded, she would have no other choice than sign the bill and put her head under the axe. Such is the logic of the constitutional monarchy in the UK, whether you like it or not. The power by Parliament over the monarch was once revealed to the monarch in full in the course of British history, with the most deplorable effect on the latter, so Queen Elisabeth II prefers to sit quiet in one of her palaces, signing every bill that Parliament kindly passes her to sign.