Individuals are now putting aside an average of £113.77 each month - or 8.52% of their income.
Both figures are higher than at any time in the last ten years.
The amounts reflect what people are putting into bank accounts or other savings products like ISAs, but exclude pension contributions.
The rise over the last year has been particularly noticeable, with monthly savings up by 9.25% over the last year.
That may well be partly explained by the rush among those over 65 to buy the government's pensioner bonds, which offer attractive rates of interest.
All other savers have had to contend with continuing low interest rates, which have reduced savings rates to as little as 0.01% a year.
"The latest results are encouraging, but we hope more people will be putting aside money into their rainy day savings, so they feel ready to deal with an emergency should one arise," said Julian Hynd, the retail director at NS&I.
The figures were based on a survey of 2,431 adults, conducted in January and February, 2015.
Britons are managing to save more money than at any time in the last decade, according to National Savings and Investments (NS&I).