Around one in three (32%) people would struggle to afford food for themselves and their family if they lost less than £500 to fraud, according to a survey.
This figure rises to 50% of people for a fraud loss of £1,000.
The research was carried out for TSB, which launched its own fraud refund guarantee in 2019 to cover people who are scammed due to making an honest mistake.
It found nearly three-quarters (74%) of people would support their bank offering guaranteed reimbursement.
Many banks have signed up to a voluntary reimbursement code to help people who are tricked into transferring money to a fraudster, but there have been concerns that some are expecting customers to have sophisticated knowledge of scams.
Other recent bank and building industry initiatives have included setting up helplines that customers can call if they receive suspect contact that could be a scam.
TSB said industry figures show that, on average, people lose £3,346 to authorised push payment (APP) scams where they are tricked into transferring money.
More than a quarter (28%) of people said their mental health would be affected if they lost less than £500 to scammers, rising to 45% if they lost £1,000.
TSB found young people are most likely to have been a victim or know someone who has been a victim to fraud in the past 12 months – with a third of 18 to 34-year-olds (32%) agreeing compared to under a fifth of 35 to 54-year-olds (18%) and 13% of over-55s.
The bank said its guarantee has refunded 98% of all bank fraud cases since April 2019, compared with 42% of funds lost to fraud being returned to the victim across the industry more widely, rising to 49% under the voluntary industry reimbursement code.
Seven in 10 (72%) people surveyed said customers should be told how their bank performs on the issue of fraud refunds.
TSB said its refund guarantee has helped it to become better informed about the nature of fraud cases due to the more transparent conversations customers now have with its fraud department – as they realise they are not being “blamed”. It argued this approach protects mental health as well as finances.
Trade association UK Finance has argued that criminals are exploiting weaknesses which are outside banks’ control – and co-ordinated action including other sectors is needed tackle what it described as a national security threat.
Debbie Crosbie, chief executive of TSB, said: “Much more needs to be done to better protect people and for industry and Government to work together to tackle this threat.”
More than 2,000 people were surveyed.
Caroline Abrahams, charity director at Age UK, said: “With so many people walking a financial tightrope at the moment, struggling to manage the triple whammy of rising household bills, cuts in benefits and the end of furlough, the very last thing they need is to be targeted by unscrupulous criminals.
“Fraud can have a catastrophic and life-changing impact, not just financially but to people’s confidence, wellbeing and relationships.
“There are still far too many cases where innocent people are conned by criminals into agreeing a fraudulent transaction, and then have to battle with their bank to get a refund.
“With only around half of victims refunded under the banking code, it is clear that it is not working as well as it should. TSB’s recognition that we can all be victims of fraud and that banks are best placed to provide protection is really welcome.”
Age UK has free information on its website to help people avoid scams.
A UK Finance spokesperson said: “Fraud has a devastating emotional impact on victims and the money stolen goes on to fund serious organised crime.
“The banking industry invests billions in advanced systems to stop fraud happening in the first place, but criminals are exploiting weaknesses outside of banks’ control, such as online platforms, to target customers. This is why we are calling for Government-co-ordinated action across every sector to tackle what is now a national security threat.”