Annual inflation as measured by the Consumer Prices Index (CPI) reached 1.8% last month, up from 1.6% in December.
It is the fourth consecutive month that the rate has risen and is the highest level since June 2014.
The Office for National Statistics (ONS) attributed the increase to rising fuel prices, which hit a two-year high in early February, and to the fact that food prices remained unchanged between December and January, having fallen a year ago.
However, the prices of clothing and footwear fell by more than they did 12 months ago, and inflation still remains below the Bank of England's target rate of 2%. It has not hit that level since December 2013.
Inflation is widely expected to rise this year as a result of the weaker pound making imports more expensive, and the Bank of England recently predicted that the inflation rate would reach 2.7% in 2018.
Meanwhile, consumer inflation as measured by the Retail Price Index (RPI) – which includes housing costs – rose to 2.6% in January, up from 2.5% in December.
Chris Williamson, Chief Business Economist at financial data firm IHS Markit, said: ‘Further upward pressure on prices looks inevitable in [the] coming months as energy costs continue to climb and firms pass rising costs on to customers, pushing inflation up towards 3.0% in the second half of the year.’