The figures from the Office for National Statistics are the latest to show the impact that storms and heavy rainfall had on the economy at the end of 2013 and the start of this year. The industrial sector's poor start to the year could be an early sign that growth in the first quarter overall will falter.
The U.K. economy grew 0.7% quarter-on-quarter in the last three months of 2013, or 2.8% at an annualized rate.
The industrial sector makes up just under one-sixth of the economy's output.
The ONS said industrial production rose 0.1% in January from December, slowing from a 0.5% growth rate the prior month. Economists in a Wall Street Journal poll had expected slightly faster growth of 0.2%.
Production of pharmaceutical products--which tends to be volatile--fell 13.9% in January from December, the biggest fall since February 1968. The ONS said the fall wasn't spread across the whole industry, but didn't provide further details.
Rises in the production of other goods meant manufacturing as a whole grew 0.4% on the month.