About 14 million people could be encouraged to save more money if a national savings strategy were set up, a report from Which? has found.
The consumer group wants the Government to work with the industry and employers to "help get the UK saving", which would involve passing on lessons from people who already have good savings habits.
It said possible ideas which could be discussed and tested out to see if they help people save could include automatically diverting someone's wages into a savings account, in a similar scheme to the Government's flagship automatic enrolment initiative, which is encouraging millions of people to save into pensions.
Another suggestion could be to remove some of the dilemma that people have as to whether to save or to pay off some of their debt, by exploring how lenders could offer an option for depositing a "token" contribution into a savings account as part of the debt repayment process.
Which? said some credit unions already do this when they lend money. By paying a small proportion of debt repayments into a savings pot, this eventually leaves consumers with no debt and a small savings buffer.
The consumer group estimates that there are around 11.5 million people who struggle to save regularly and a further 2.5 million people who do not save but who could afford to, who could be encouraged to save more, making 14 million in total.
Households are recommended to have at least three months' worth of essential expenditure shored up that they can turn into cash to protect against sudden income shocks.
But Which? said that four in ten (41%) people say they could not last three months without their main source of income.
It said households without a three-month buffer are significantly more likely to have defaulted on a payment in the last month or used high-cost credit like payday loans.
The consumer group estimates that half the population (49%) are unhappy with their level of household savings and a quarter (24%) have no savings at all.
It also identified key features of successful savers, which could be harnessed to help others.
People who tend to have the most success in building up a pot of cash tend to save regularly each month, save for a "rainy day" rather than a specific goal such as a holiday or a car, and keep their savings separate from their other money, taking away some of the temptation to dip into their nest egg.
Which? executive director Richard Lloyd said: "With half the population unhappy with their level of savings, and a financial buffer so crucial to the resilience of households and the wider economy, we're calling on the Government to help get the UK saving.
"We've looked at the most successful savers and identified the behaviours that the industry and Government should be encouraging to help those who can afford to save, save more."
Which? used various sources for its research, including a survey of 4,000 adults.
Last month, the Government almost tripled the amount of cash that could be saved tax-free into an Isa. The new "super-Isa" allows people to save up to £15,000 a year tax-free in cash, stocks and shares, or any combination of the two.
It also announced radical reforms in the Budget to give people more freedom over how they cash in their pension pots.
A Treasury spokesman said: " The Government welcomes this report - we have taken radical steps to support hardworking people as they take long-term decisions to save for their future.
"At Budget 2014, we announced fundamental reforms which will provide increased choice and flexibility and help all savers, at all stages of life.
"We reduced taxes for the lowest income savers, reformed the Isa regime to give all savers greater flexibility over where and how they save their money, and announced the creation of new products to help retired savers see a better return.
"The Government also welcomes progress made by industry to bring simple financial products to market."