It is the third time UK industry has been in recession in eight years.
Although industrial production rose 0.3% from February to March, it fell 0.4% both in the first three months of 2016 and in the last three of 2015.
Compared with a year ago, manufacturing production in the first quarter fell 1.9%, the biggest fall since 2013.
The biggest fall in output came from the  basic iron and steel sector which saw production drop in March by 37.3% percent compared with a year earlier.
However, the oil and gas industries saw sharp gains, increasing production 17% in February, and 10.9% in March from the same months a year earlier.
Manufacturing and construction is proving to be a drag on the whole economy, helping slow UK economic growth from 0.6% in the last three months of 2015 to  0.4% between January and March, according to the ONS.
Earlier this month a survey by Markit/CIPS also showed manufacturing contracting. Chris Williamson, chief economist at Markit said: "The goods-producing sector therefore looks to be on course to act as a drag on the economy again in the second quarter, contributing to a slowing in economic growth to near-stagnation.
"Growth could be even weaker if the surveys disappoint in coming month, which seems probable given the intensifying uncertainty over the outcome of the EU referendum."
Despite this, economist Ruth Miller from Capital Economics is optimistic for the rest of the year.
She said: "We still expect things to look up as the year progresses. Sterling's recent depreciation and our expectations that global growth will pick up slightly in 2016 should allow the sector to return to modest growth later this year."
UK industry fell back into recession as it shrank for the second quarter in a row, according to the Office for National Statistics (ONS).