The ban has been made under the "order of the Secretary of State," which comes under the Air Navigation Order 2009, set out by the UK's Civil Aviation Authority (CAA). This legislation includes a broad set of rules that restrict drone flight in the UK; for instance, a drone must always be within 400 vertical feet and 500 horizontal meters of its pilot. If the unmanned aerial vehicle (UAV) has filming capabilities, additional rules limit how close it can be flown to other people. An order from the Secretary of State, however, can restrict the use of drones in crowded places, or if there's a chance unsupervised flight could affect national security. In this instance, it seems to be the former, as a Royal Parks spokesperson told the Times they could impact the local wildlife and make visitors uncomfortable.
Ever since a UAV crash-landed in the White House's grounds -- not to mention the mysterious sightings around Paris -- there's been a growing consensus that tighter drone controls are necessary. The House of Lords EU Committee is already debating tougher guidelines that would affect drone ownership in the UK; until they become law, we're probably going to see more signs like this one cropping up around Britain.