From an aviation law perspective there is no prohibition of UAVs (or UAS Unmanned Aircraft Systems as they are now commonly known). If they meet the relevant requirements then they can fly - the problem is that there are few requirements specific to this type of vehicle. The CAA regulates most aspects of UAS operation and provides guidance in
CAP 722 - it's just been updated but unless things have changed significantly it can be summed up by saying:
(a) if there are existing requirements that apply, a UAS must comply with them
(b) if there are existing requirements that would apply to a manned aircraft that you do not think are needed for a UAS, you must explain why and get agreement from the CAA, and
(c) if there are aspects of the operation that are not covered by existing requirements but present risks (to other airspace users or 3rd parties on the ground etc.), you must present arguments as to how those risks will be managed, i.e. present a safety case.
Hope this helps.