Four men convicted of murder and robbery for heist that left eight guards dead.
The body is the third to be returned.
The corpses of two other men were handed over to the UK in June.
The two other captives – IT consultant Peter Moore and Alan McMenemy – remain missing.
The UK believes that Moore, who was being protected by the security contractors at the time of their capture, is still alive.
Brown called on the hostage-takers to release Moore and confirm the fate of McMenemy.
The Shia fighters were dressed as Iraqi policemen when they seized the group.