Are there rules about using the "Fasten seatbelt" sign outside of take-off/landing/turbulence? Related to this question regarding flight attendants continuing to stand during turbulence. 

My understanding is that it is the law for passengers to be seated with their belts fastened during taxi/take-off/landing along with the flight attendants. 

At other times during the flight, the fasten seatbelt sign is also illuminated at times of turbulence/expected turbulence (as per the question linked above, and usually accompanied by a warning from the captain that they're expecting turbulence) - I assume this is subject to the same rules that insist passengers are actually seated during these periods. 

On several recent flights on budget airlines (Ryanair/EasyJet), I've begun to notice that the crew are using the fasten seatbelt sign in order to ensure passengers are seated whilst they're serving food/drinks etc. This was confirmed when I was sat at the front of the plane and over heard the cabin crew discussing this. 

Clearly, there is a good rationale for keeping passengers seated whilst hot drinks are being served as the aisles on budget planes are too narrow to easily squeeze past, but on Ryanair/EasyJet flights there are also significant times when cabin crew are simply trying to flog cheap perfume and scratch cards. 

During these recent flights where the fasten seatbelt sign was illuminated unnecessarily for long periods of time, passengers begun to simply ignore the signs in order to make use of the toilets (especially people with young children etc).

Are there rules that govern when pilots/crew may illuminate the fasten seatbelt signs, and are the passengers breaking any laws by ignoring them?
You dont have a jurisdiction tagged (although it sounds like this is an EASA matter) your answer may vary depending on where you are asking for. I can answer for the US/FAA. 

Here in the states you are technically in breach of an FAA FAR by not remaining seated. As per FAA FAR 121.317


  Sec. 121.317
  
  Passenger information requirements, smoking prohibitions, and additional seat belt requirements.
  
  ....
  
  (f) Each passenger required by Sec. 121.311(b) to occupy a seat or
  berth shall fasten his or her safety belt about him or her and keep it
  fastened while the "Fasten Seat Belt" sign is lighted.
  
  .....
  
  (k) Each passenger shall comply with instructions given him or her by a crewmember regarding compliance with paragraphs (f), (g), (h), and (l) of this section.


I cant find a regulation on using it in times its not otherwise required by FAA FAR 121.311 but this discussion seems to elude to the fact its at the "Captains Discretion".