The number of usable seats that have to be reduced is set out in the Minimum Equipment List or MEL. It is a controlled document by Boeing, the FAA and for the UK the CAA. It lists the procedures to be used to deactivate the door including the mandatory signage required even though it looks unsightly. It also lists any procedures the crew have to accomplish, such as ensuring a certain number of seats are not occupied in a cabin zone.
The MEL also sets a time,flights/cycles limit for each item that is allowed to be unserviceable. The System BA uses takes the info from the Tech Log and BA Maintenance and makes it available for Ops staff and Flightcrew to view prior to a flight. In this way Load or Departure control can block off seats, or use their voodoo magic to 'seat shift', that all time popular act on this board, to ensure limitations are complied with prior to boarding.