The Germanwings Airbus A320 from Barcelona to Dusseldorf crashed in France yesterday after an eight-minute rapid descent, killing everyone on board.
"We cannot rule out the possibility that other British people were involved in the crash," Philip Hammond said.
A 37-year-old UK resident, Marina Bandres Lopez-Belio from Manchester was on the flight with her baby son Julian.
"We are devastated and would like to request that we be allowed to grieve in peace as a family without intrusion at this difficult time," said Marina's husband Pawel Pracz.
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Hammond said families of those from the UK known to have been killed in crash of the airliner operated by Germanwings, have been contacted.
"This accident is a terrible tragedy and I want to offer heartfelt condolences to the families and friends of all those involved in the accident," Hammond said.
Prime Minister David Cameron and Labour leader Ed Miliband have offered their condolences to the families of those affected by the air crash.
Officials believe 67 of the 144 passengers on the plane were German citizens, including 16 pupils returning from an exchange trip.