Doctor Richard Payne, a lecturer and environmental scientist at the University of York, has been confirmed as one of the missing eight climbers, which also includes four Brits.
Five bodies have since been spotted during the hunt for the climbers by Indian air force pilots.
The rescue operation was suspended on Monday due to severe weather conditions, officials said.
The operation is expected to resume on Tuesday.
The group disappeared in the Nanda Devi region of the Himalayas following an avalanche.
The team, led by British mountain guide Martin Moran, was attempting to reach the top of an unclimbed peak in a remote area.
Four other British members of the expedition have already been rescued.
Searches have been taking place in a bid to find the missing climbers after the alarm was raised on Friday morning.
They were last in touch with base camp on May 26, now more than a week ago.
District magistrate Dr Vijay Kumar Jogdande said the bodies were found on Monday before the rescue operation in the northern state of Uttarakhand was suspended because of heavy snowfall and high winds.
A University of York spokesman said they remain extremely concerned for Dr Payne's safety.
A spokesperson from the University of York 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 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."