The survey, published yesterday by the Chartered Institute of Purchasing and Supply (CIPS), also showed a slowdown in the rates of increase of new orders and employment.
CIPS's purchasing managers' index for UK manufacturing, which measures changes in output, new orders, employment, suppliers' delivery times and stocks of goods purchased, fell from 57.2 in June to 55.4 in July on a seasonally-adjusted basis. This was the lowest reading in a year.
However, although the July reading signalled a significant slowdown in growth and was adrift of the 57.2 figure forecast by economists, it remained well above the level of 50 which separates expansion from contraction in CIPS's survey.
CIPS's output index for UK manufacturing fell from 59 in June to 57.2 in July - its lowest level in more than a year. The survey showed an easing of growth of manufacturers' overall new orders to the slowest pace since March. And the rate of expansion of new export business slowed to its weakest in four months.
The UK manufacturing workforce rose in July at the slowest pace in nine months.
The slowdown in manufacturing growth coincides with increased speculation that the first rise in UK base rates from their record low of 0.5 per cent, where they have been since March 2009, is not far away.
Rob Dobson, senior economist at survey compiler Markit, believed the report showed the UK manufacturing sector started the third quarter on a firm footing.
He noted growth rates for production and new orders, although they had cooled in July, remained well above their long-run trends, supporting continued solid job creation in the sector.
However, reflecting on the slowdown in growth, he said: "The concern is that the slowdown we are seeing is also a symptom of increased economic uncertainty both at home and in key export markets of Europe, in turn fuelled by worries about the Ukraine crisis. If the situation with Russia deteriorates further, we should expect goods exports to come under further pressure."
He added: "It remains too early to gauge the impact of the Ukraine crisis, but the worry is that the combined effects of expected policy tightening, heightened economic uncertainty and sluggish trade could mean manufacturing growth could suddenly weaken more than expected."
Many economists are predicting the first rise in base rates will come later this year or in early 2015.
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "The softer manufacturing purchasing managers' survey will fuel expectations that the Bank of England will hold off from raising interest rates until early 2015, rather than act late this year. However, it remains a very close call and much will clearly depend on what happens with wage growth over the coming months, as well as the economy's overall performance."
Looking ahead to the Monetary Policy Committee's meeting next week, he added; "What is certain is the Bank of England will keep interest rates at 0.5 per cent at the end of the August MPC meeting on Thursday."
Andy Hall, head of corporate banking in Scotland for Barclays, said of CIPS's survey: "The dip in July's index should not detract from an overall level of performance which is still consistent with strong growth. The picture of a healthier manufacturing sector continues to emerge with above-trend rises in new orders, output and job creation."
He added: "Broadly supportive economic conditions as well as a more favourable R&D (research and development) environment, helped by the recent increase to tax credits, are encouraging manufacturers to invest more in both new product development and process enhancements."
CIPS chief executive David Noble said: "Manufacturing delivered a less remarkable batch of results at the beginning of Q3 in an otherwise vintage year. Export orders, output and employment have continued their upward charge, but the sector has lost some fizz, as all three return to more pedestrian rates of growth this quarter.
"Nevertheless, it is a mark of how far manufacturers have come that the lowest PMI in a year is still well over the long-run survey average."