UK annual inflation measured by the Retail Prices Index (RPI) went negative in March for the first time since 1960, to -0.4%, down from zero in February.
RPI includes mortgage costs, which have fallen following the Bank of England's reductions in interest rates.
The Consumer Prices Index (CPI), fell in March to 2.9% after February's unexpected rise to 3.2%, the Office for National Statistics (ONS) said.
The official CPI figure is still well above the government's target of 2%.
The ONS said that the biggest downward pressure on inflation had come from energy prices as the price of oil was significantly below the level it had been in the same month last year.
Rob Pike, an economist at the ONS, said further reductions in energy prices would have an effect on April's figures.
"Clearly on the horizon there are downward pressures," he told the BBC, citing further energy price cuts which are due to come into effect.
Vegetable imports from Spain revived, sending vegetable prices lower, after being hit in the previous month by poor weather conditions.
Transport costs also fell as a result of lower fuel prices, which also fed into lower air fares.
Items in the ONS basket that were more expensive included the games, toys and hobbies category, with the price of computer games rising.
Kevin Peachey, personal finance reporter, BBC News
For those UK residents with a mortgage, the cost of living fell in March compared with a year earlier - but that does not give a complete picture of deflation. So who benefits?
Older people have just had a 5% rise in their basic state pension - so if prices rise by less than 5%, in theory they will be better off.
However, many pensioners rely on the interest on savings to top-up their pensions and these returns have dropped sharply.
One blow would be for workers' wages. If employers take RPI into account when deciding on any pay agreements, then a pay freeze is the likely result. The real value of their wage will arguably be higher though.
Graduates who took out student loans before 1998 may even get a rebate as their interest payments are set according to March's negative RPI rate.
The price of clothing was also up from a year ago, with women's outerwear a particular driver.
While the CPI is important as the rate that is targeted by the Bank of England's interest rate-setters, the RPI is used by many companies as the starting point for wage bargaining.
TUC general secretary Brendan Barber has warned that the negative RPI figure should not be taken as an excuse to freeze wages.
"Although in some workplaces unions have agreed to put pay increases on hold or take cuts in wages to save jobs, many companies are still profitable and able to afford decent pay rises," he said.
"Widespread wage freezes would prompt families to cut back on their spending, which would be the last thing the UK's struggling economy needs right now."
The RPI is also the figure that determines what happens to benefits and the basic state pension.
The figure used for pensions will be the one that comes out in September, although there is a minimum increase of 2.5%.
But it is the March RPI figure that is used to determine the interest rates paid on student loans.
The new rates will be announced between now and when they take effect in September.
People who have outstanding debt from student loans taken out before 1998 may even end up with a negative interest rate. The government is currently considering whether they could be due a rebate.
It has more flexibility in setting rates on loans taken out after 1998.
There are signs that inflation could fall further before September.
"We suspect that the weakness of retail spending and activity in general will bear down strongly on core inflation in time," said Jonathan Loynes at Capital Economics.
"UK inflation is still set to drop a lot further and the threat of a broader bout of deflation has not evaporated."
Michelle Mitchell, charity director of Help the Aged and Age Concern said: "Falling headline inflation masks the fact that that many older people's real rate of inflation remains far higher than the average.
"With up to £5 billion of benefits going unclaimed by pensioners every year, we are strongly urging older people to ensure they are getting all the support they are entitled to."
There was a warning from the British Chambers of Commerce of the challenges posed to the chancellor by the downward trend in inflation.
"Deflationary pressures could make the recession worse in the short-term, despite quantitative easing and the huge budget deficit posing inflationary pressures over the medium-term," said the organisation's chief economist David Kern.
"The chancellor must address both these conflicting risks in his Budget."