However, manufacturing continued to lag behind, falling by 0.6% last month after a fall of 0.4% in April.
Manufacturers have struggled against the strength of the pound and weak demand in European markets.
The numbers suggested “a persistent weakness” developing in manufacturing, said UBS economist David Tinsley.
“The last few months’ readings of manufacturing output have been soft, and surveys such as the PMI are also suggesting slower growth,” he added.
Compared with a year earlier, industrial output rose by 2.1%, the strongest annual growth since April of last year, and manufacturing was up 1.0%.
George Osborne is expected to announce more help for manufacturers in his Budget announcement on Wednesday.