Manufacturing output fell by 0.2% compared with April, according to the Office for National Statistics (ONS).
On a yearly basis, industrial production dropped unexpectedly by 0.2%, but slower than the 0.8% decrease seen in April.
BoE rate-setter Michael Saunders this week said he was "reasonably confident" that an improvement in exports and investment would more or less compensate for the consumer slowdown.
Separate data from the ONS showed that the UK's trade deficit widened in May.
Germany's industrial production grew at the fastest pace in three months in May, Destatis reported Friday. Economists surveyed by The Wall Street Journal forecast a 0.3% rise.
Things looked a little brighter in terms of volumes of goods exported in the three months to May, which rose 3.8 percent. Business sentiment hit a record high in June, measured by the Ifo Institute's monthly survey.
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Similarly, manufacturing output dropped 0.2%, offsetting a 0.2% rise in April.
The ONS also released figures for construction in May, which were much worse than expected.
This was the largest growth since February, when output climbed 1.5%.
"With these outturns coming on the back of several months of soft data, it is now virtually certain that both [the industrial and construction] sectors will drag on GDP growth in the second quarter", said Howard Archer, chief economic adviser to the EY Item Club.
Capital Economics analyst Jennifer McKeown said the data supported expectations that the German economy accelerated sharply in the second quarter after expanding by 0.6 percent in the first three months of the year.