I didn't see theDiscovery programme, but here is a litttle known giant myth that might interest you:

Inside the gate of Weston churchyard in Hertfordshire, there are two stones 14 ft apart. They are said to be the grave of Jack o'Legs, the Weston Giant. He was a local robber who was a bit of a folk hero too "robbing the rich and giving to the poor" etc.. Earliest written account is 1728.

After his death and internment in his 14ft long grave, Weston became a place of pilgrimage (or tourism if you prefer). Parish clerks would show the very long thigh bone of Jack for a tip! Eventually this bone went to the Ashmolean where it was discovered to be the femur of an elephant. As for Jack's grave - the stones are the foot stones of two separate graves!

There have always been exceptionally tall people and giantism is a medical condition still with us. Relativity will also be a factor eg the naturally tall Watusi of Kenya (?) would look like giants to Congolese pygmies if they ever met. Maybe in Britain there were impressive height differentials between indigenous and immigrant communities.

I feel sure though that most of the "giant races" myths come from later people, with diminished technical abilities, attempting to explain the existence of megalithic and other massive constructions. "We couldn't build that (Stonehenge, Acropolis, Roman aqueduct etc) - so no ordinary men could build it - so the gods/giants MUST have built it" Some people still claim that of course - the Pyramids of Giza, Stonehenge, Nazca lines are all built by aliens - the new giants. They even say that we do not have the technology to build them - even today. Same myth in a new guise.