Soaring prices for bread, cereal and chocolate meant the cost of living rose more than expected last month.
Inflation, which measures the rate of price rises, fell to 10.1% in the year to March from 10.4% in February.
It was widely expected to fall below 10%, but food prices continued to soar, rising at their fastest rate in 45 years.
Falling inflation doesn't mean prices are falling, but just that the rate of price rises is slowing.
Grant Fitzner, chief economist for the Office for National Statistics, which provides the figures, said globally food prices were falling, but that had not yet led to price cuts.
"There's been some strong upward movement in food prices and you would expect to see that reflected in supermarkets but we're not there yet," he told BBC Radio 4's Today Programme.
When asked whether we might see double digit inflation sustained at least for another month with food prices continuing as they are, he said: "It is certainly within the realm of possibility but we don't forecast this."
Chancellor Jeremy Hunt said he was still confident that inflation would fall sharply by the end of the year.
He added: "We have a plan and if we're going to reduce that pressure on families, it's absolutely essential that we stick to that plan, and we see it through so that we halve inflation this year as the Prime Minister has promised."
But Rachel Reeves, Labour's shadow chancellor, said: "The reality is that under the Tories our economy is weaker, prices are out of control and never have people paid so much to get so little in return."
Inflation in the UK remains higher than in other Western countries, including the US, Germany, France and Italy.
Factors behind this include the UK's exposure to rises in wholesale gas prices, its reliance on imports of certain foods, and worker shortages and wage rises.
One of the main reasons inflation was higher than expected in March was that food prices continued to surge.
The war in Ukraine drove up food prices around the world, with the prices of grains and vegetable oils soaring. Rising transport and packaging costs are also making imports more expensive.
Wholesale food prices have started to fall, but it usually takes some time before that feeds through to the supermarket shelves.
The sharpest rises in March were seen for products including olive oil (up 49%), milk (up 38%) and ready meals (up 21%).
While food prices remained stubbornly high, petrol prices eased, bringing some relief for motorists.
Unleaded petrol prices peaked at about £1.90 in July and were down below £1.50 in March.
Simon Mellin, founder and chief executive of The Modern Milkman, a milk delivery service, said the food industry had faced soaring costs in recent months, with milk, eggs and packaging prices all going up.
He believes that food prices will start to stabilise, but will remain at a much higher level than they were this time last year.
"I'm really unsure if food prices will drop as much as everyone expects," he told the BBC.
"I expect some reductions but I wouldn't personally expect huge reductions in the next twelve months."
He said he was trying not to pass higher prices onto customers, but added that it was a balance the business had to tread.
The Bank of England has been raising interest rates to try and curb inflation. In March, the Bank increased rates for the eleventh time in a row, taking the main rate to 4.25%.
The idea is that when people have less money to spend, they buy fewer things, reducing the demand for goods and slowing price rises.
Following the latest inflation figures, Luke Bartholomew, senior economist at abrdn, said a further rate rise next month is now "likely", with inflation pressures proving "more persistent than the Bank of England expected".
Rate rises mean higher mortgage payments for some homeowners and those with loans. But they can also benefit savers if banks pass on the higher rate to customers.
Source: BBC