Ever since the English Civil War and the short-lived Puritan Republic, the institution that clipped the Sovereign's wings has been Parliament. James I and Charles I (both Anglican) stood on Divine Right and they lost.
Lest you think that Parliament is a fount of freedom, consider the fact that the next Sovereign to be deposed was James II. He actually did nothing to injure the rights of Englishmen. What got Parliament in an uproar was the fact that he was a Roman Catholic, even though he did his duty as Supreme Head of the Anglican Church and tried his best to live up to his oath as Defender of the Faith. To be blunt, James II did something for freedom by separating his conscience from his duties. His compromise was that he worshipped Roman Catholic as a private person but administered the Anglican Communion while "on the job." In so doing, he established the idea that a person's religious conscience is his own when off the job.
Fact is, he was deposed because he was a Roman Catholic and had sired an heir. Had his line continued, the prerogatives of the Anglican Church would have been eroded. The Glorious Revolution, regardless of its benefits, was not a blow for freedom.
This capsule revisionism of mine ties in with Dr. Gabb's point - namely, that the instrument that used to hem in the Sovereign is, as of now, no prize for the freedom-loving. But, that leads to the question of what is to be done.
There's only one option left: to petition the same group that was responsible for bringing King John to heel via the Magna Carta. It was this group of worthies who restrained the Sovereign when Parliament was little more than a gaggle in the Sovereign's back pocket. It's the only institution left if Parliament is little more a gaggle of little tyrants.
As I said, I don't think Dr. Gabb has quite thought through his complaint. If pursued to "what are you going to do about it?", it leads to either revolution (which he eschews) or counting on the hereditary aristocracy to step in.
Come to think of it, we haven't heard much from them lately...
Mr. Gabb is fully aware that he is demanding that the Royal Sovereign stand up for the rights of her subjects and due her duty to protect them, even if her title what has become a gilded cage is imperiled. Parliament, the BBC, and Brussels are trying to destroy traditional Britain. There already is a Constitutional crisis, and there is neither consent of the governed nor a pretense of legitimate authority.