How many times has Her Majesty had to issue gag orders to the press since taking the throne?
no but she can wave at them and cut ribbons to their new buildings
She doesn't have that power.
She only has to flash the press to make them gag She can only make a request, but, she is highly respected and if any member of the press didn't honor her request and it got out to the people, that person's career would be over.
In theory she can. She IS the Queen, after all, and thanks to the unwritten nature of the British Constitution, she can do anything that isn't specifically prohibited - and this isn't. But she never has done so - the fact that she had done so would be reported in the press and bring her even more bad publicity than just letting the story go ahead anyway. The British government occasionally issues DA Notices (Defence Advisory Notices) to the press requesting them not to report certain matters relating to national security. But even those are only requests, not gagging orders. It would just be wrong to make it a criminal offence to report these matters and the public outrage first steps towards a dictatorship and all that would be possibly even more damaging. Nevertheless the British press is basically responsible and always complies because it knows the damage that would result to itself and the country if it didn't. If nothing else, a press organisation or newspaper that didn't comply would quickly find itself disrespected, bankrupt and out of business. As with so many things British, so much is unwritten but we know how to play the game - and that's why so much remains unwritten. It doesn't need to be.