The paper quoted the British Embassy in Cairo as saying that the team has entered the Nile, stretching for 6695 kilometres, at its mouth to the sea and the journey up the river is expected to finish by late December.
The expedition is the first ever ascent of the world's longest river, the embassy said.
The expedition will follow the Nile through Egypt, Sudan, Uganda, Tanzania, Rwanda and possibly Burundi.
The team are using three motorised inflatable boats, and will fly the boats over the most dangerous sections of the Nile by attaching them to a microlight aircraft.
They said wild animals and approval to cross borders were the main challenges they expected on their trip.
"The crocodiles and hippos are the most fearsome and aggressive animals on the Nile," British co-leader Neil McGrigor said.
"You give them a wide berth."
- NZPA