StepChange argues that saving £1,000 would protect 500,000 households from falling into problem debt.
It said low-to-middle income groups, tenants, and parents with young children were least likely to have the savings buffer.
They should be prompted to save through a system that diverts money from wages.
Mike O'Connor, chief executive of StepChange, said: "Our research highlights a national savings crisis with far too many families living without a financial safety net and at real risk of problem debt.
"Adapting the existing approach to pension saving would ensure each adult is better able to cope with an unexpected bill and a loss of income without sinking into debt."
The charity argued that workers should be able to divert money that is automatically routed to pension savings into an accessible pot for emergencies.
Other incentives, similar to schemes used overseas, could include savings accounts which give savers the chance to win cash prizes. This appealed to those on low incomes, StepChange argued.
It also raised the idea of renewing matched savings, which saw a government top-up when households put money aside in specific accounts.
