In easyJet it is the PF that sets it above MSA. Not many captains appear to know that though. In descent it is set back to destination QNH by PF by FL200.
From easy OMB:
When cleared to a Flight Level PF will order PFD altimeters to be set to Standard. PNF will set STANDARD and crosscheck both PFD's. The PF will set the ISIS altimeter to Standard when above the relevant MSA. This action may be delegated to the PNF. Care must be exercised to meet altitude constraints before pulling standard especially in low pressure conditions.