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According to a study from Markit and the Chartered Institute of Purchase and Supply, the Purchasing Managers Index rose to 45.4 last month, an increase on the 43.1 figure recorded in April.
The sector shrank at its slowest pace for a year during the month and three consecutive months of growth have now been recorded, a fact that was welcomed by ING economist James Knightley.
"Today's data will bolster hopes that the UK economy may recover more swiftly than had previously been expected," he told Reuters.
However, Mr Knightley warned that rising unemployment and debt levels, coupled with the increasing value of sterling, means growth is likely to be "extremely fragile".
In related news, the Confederation of British Industry recently revealed that UK retail sales fell during May, as almost half (48 per cent) of retailers questioned saw a decrease in their year-on-year sales.
