Are passengers allowed to travel seatless(on the floor)?
Passengers on commercial airliners (US, EU, Canada, most of the world) aren't allowed to sit on the floor because 1) they could block the aisles and emergency exits and 2) they cannot be buckled up, putting their and others lives at risk. 

That does not mean it could not have happened, just if it did it was against regulation. 

There are cases where commercial passengers may sit on the floor but they are rare, for instance parachuting. 

EDIT: In the BBC article cited after the original post says that the passengers were given spare crew flip-up seats for take-off and landing, but had to sit on the floor the rest of the time so the crew could do their service. This is against regs as they would not have been secured against unexpected turbulence. The article says the following which proves my point:


  The Civil Aviation Authority says while passengers are allowed to sit
  in crew seats under certain conditions, they must not be left unseated
  during any stage of the flight.