Nearly three-quarters of those questioned online for the Red Cross said they had already been through a period of crisis in their lives.
And 37% thought they could suffer one again within the next five years.
The main worries for people as they get older were cited as being the loss of independence and not being able to cope on their own.
About a quarter of the 2,043 people surveyed were concerned they would not be able to get around in the same way, and would be lonely and isolated.
A significant minority, about one in eight, said they felt those in the UK did not suffer crises in the same way as people in other countries.
The charity, which offers help and support in the UK as well as abroad, said support for the elderly would become “more vital” with an ageing population, shrinking budgets and health and social care services “struggling to meet demand”.
The chief executive of the British Red Cross, Sir Nick Young, said: “We understand that every crisis is personal and can have a lasting impact on the individual affected.
“There are a growing number of people facing crisis in this country and our research shows over 30% of people would be reluctant to turn to a voluntary organisation because they are embarrassed to ask for help, or a fear of diverting resources.”
A recent survey for the BBC suggested as many as half of all England’s adults experienced feelings of loneliness.
Nearest tube – Elephant & Castle underground station (Northern and Bakerloo lines).
Nearest Railway Station – Elephant & Castle
Buses from Elephant and Castle – ask bus driver for Burgess Park. Bus numbers: 12, 171, 148, 176, 68, 484, 42, 40, 45