Discretion, or as it is more correctly termed Commander's Discretion, can allow the Aircraft Captain to extend the working day within certain limits. They can also elect to reduce the rest requirement, again within preset limits. The use of this discretion cannot force crew to extend their hours beyond their industrial limits but within those limits the crew cannot refuse discretion, should the commander elect to use this option. Commanders must take into account the condition of the crew and what preceding duties they may have undertaken, more a problem away from LHR when conducting a series of flights. Taking into account, also means thinking ahead as to what duty is expected to be undertaken and what the condition of the crew may be at the end of the projected duty. A good commander will take into account the views of their crew, this does not mean allowing the crew to dictate what will happen as the crew do not have this authority.
Hope that long winded and convoluted explanation of extending a duty is helpful.