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.