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The increased saving is believed to be a response to higher interest rates and a sluggish housing market, which have made people wary about adding to the existing £1.1 trillion debt mountain.
"The consumer is more cautious than a year ago, with income growth having slowed, house prices having steadied and interest rates being up," said David Dooks, of the British Bankers' Association (BBA).
"In future we are likely to see much more subdued growth in personal borrowing, overdrafts and credit cards."
The figures tie in with claims from retailers that the high street is suffering its worst downturn in a decade, and with recent weak data on consumer spending more generally. Car sales are dropping and the housing market has stagnated.
The BBA figures, which cover most banks, showed a net repayment of £40m of credit card debt last month, the first overpayment since May 1994. In April last year, by contrast, Britons took on an additional £624m of debt.
A spokesman for Citizens Advice said: "It's too soon to see whether this is a trend that will be continued, but there's certainly no let-up in the numbers.....continued below
"We currently help around 1.1 million such people each year and that figure shows no sign of diminishing. Credit card problems account for the biggest single group: 20% of clients in serious debt are only there because they can't meet their credit card commitments."
The BBA said net mortgage lending, which does not include remortgaging, rose by £4bn last month - down from £4.5bn the month before, and the lowest figure since February 2002.
Mr Dooks said the timing of Easter could have distorted seasonal adjustment methods for both mortgage lending and credit card figures, but the trend was unmistakable.
"The weaker recent picture of mortgage demand continued in April, and tied in with other reported indicators of a slower housing market," he said.
The Building Societies Association said £1.4bn went into savings accounts last month, the most for four years, even allowing for the Isa rush in April.
The BBA reported savings deposits of £3.4bn last month, similar to March's high and £1bn higher than April last year.
There has been concern on the Bank of England's interest rate-setting panel that people are still taking on debt too readily. But if the Bank's own figures, due at the end of the month, match those of the BBA, it becomes more likely that the next rate move will be downwards.
Guardian Unlimited © Guardian Newspapers Limited 2005