The group, including Doctor Richard Payne, a lecturer and environmental scientist at the University of York, disappeared on May 26, in the Nanda Devi region of the Himalayas after an avalanche.
Led by British mountain guide Martin Moran, the team was attempting to reach the top of an unclimbed peak in a remote area.
Four other British members of the expedition have been rescued.
District magistrate Dr Vijay Kumar Jogdande said the bodies spotted on Monday are thought to be from the missing expedition and are presumed dead.
The search for the remaining three mountaineers was suspended due to poor weather conditions.
Dr Jogdande also said state officials have devised a plan to use helicopters and a ground team to retrieve the bodies and search for the others.
However this needs approval from the Indian government in New Delhi due to the difficult terrain and risk of another avalanche.
Maninder Kohli, a mountaineer who runs a trekking company from New Delhi that has taken groups to Nanda Devi East base camp, said the snow level in the Indian Himalayas this year has been "abnormally high".
He added: "Apparently the walk up to the base camp alone was a tedious task because of the snow accumulation."
A University of York spokesman said they remain extremely concerned for Dr Payne's safety.
In a statement, the university said: "Dr Richard Payne is a lecturer in our Department of Environment and Geography.
"He is among a group of climbers currently listed as missing in the Himalayas. Everyone at the University of York is enormously concerned by the latest reports.
"Our thoughts remain with Richard's family, friends and colleagues at this difficult time."
A spokeswoman for the Foreign Office previously said: "We are in contact with the Indian authorities following reports that a number of British nationals are missing in the Indian Himalayas.
"We will do all we can to assist any British people who need our help."