We have been lead to believe that much of the power that was once held
by the monarchy has been transferred to the Parliament and that the
Queen is mostly a figure head.
This is wrong. Even if the Queen did not use their powers against the desire of the Cabinet and Parliament, it was mostly because the Cabinet and the Parliament do not express wishes contrary to the will of the Queen. If they did, they would be dissolved.
So bearing in mind the real powers invested in the Queen, they just follow her line, which she expresses softly, in private conversations with ministers.
Great Britain is in fact an absolute monarchy with some elections allowed (similar say, to Qatar or Saudi Arabia), with a claim that the Queen is just a figurehead being a successful propaganda tool.