Philip Hammond, the Chancellor, blamed the weather.
"Today's data reflects some impact from the exceptional weather that we experienced last month, but our economy is strong and we have made significant progress," he said.
However the ONS said the snow is a small part of the picture.
"While the snow had some impact on the economy, particularly in construction and some areas of retail, its overall effect was limited with the bad weather actually boosting energy supply and online sales," said Mr Kent-Smith.
GDP per head fell by 0.1 per cent quarter on quarter, the first drop in two years.
The construction sector's output plunged by 3.3 per cent, dropping in every month - not just those with the worst weather.
Manufacturing slowed to grow by just 0.2 per cent.
The 'Beast from the East' weather front hit hotels and restaurants, damaging the dominant services sector, which expanded by a sluggish 0.3 per cent - though the ONS found little evidence of the snow causing the slowdown in the wider industry.
Production industries rose by a more impressive 0.7 per cent, as the oil and gas sector rebounded from pipeline closures late last year, and families turned up the heating.
The Bank of England had anticipated a smaller slowdown, last month cutting its forecast to 0.3 per cent after the snowy spell.
Markets - which at the start of this month were almost certain of a May rate hike - now think the next increase could be delayed until September.
The pound slumped by 0.8 per cent against the dollar as a result, to $1.3815.
"It seems inconceivable to us now that Mr Carney will vote for a hike at the next meeting, and while other members may hold different views, it is hard to imagine any but the most hawkish deeming a hike in May to be appropriate," said John Wraith at UBS, predicting the Monetary Policy Committee will vote to hold rates.
"With inflation likely to return to target within the next three to six months, we believe the case for higher rates will look increasingly threadbare from both real activity and inflation standpoints. For us, it means no hike at all in 2018."
Economists hope for an improvement in growth in the coming months.
On a monthly basis, the estimates indicate overall GDP growth was better in March than in February even though the worst of the cold came in the later month, which may hint an improvement is on the way.
"The slowdown in services was not broad based – it was concentrated in the retail sector which tends to be hit hardest by bad weather," said Paul Hollingsworth at Capital Economics.
"As a result, this slow patch should prove to be transitory, if past experience is anything to go by."
But now Mr Carney and his colleagues have to judge whether or not this more severe crunch will have a longer-term effect on the economy.
One factor harming growth has been the fall in household spending power, as inflation outstripped wage rises for much of the past year, largely because the weak pound pushed up import costs.
But that pressure should now be over as earnings are once more outpacing prices, which should improve the economy's prospects.
Employment is also at a record high, which should support household spending.
"Much of the activity lost to the bad weather in the first quarter should eventually be made up," said Howard Archer, chief economic adviser to the EY Item Club, predicting growth will rebound to 0.5 per cent for the second quarter.
"Growth over the rest of 2018 should be helped by the squeeze on consumers easing as the year progresses."
