"A softening of new orders suggested some hesitancy from the United Kingdom to commit to new projects, which will be a worry as the domestic market has been the main driver of growth in the past two months", said Duncan Brock of CIPS.
Input and output prices both showed renewed increases although the inflation was cooler than the beginning of the year.
Markit added the slowdown was broad-based, encompassing the consumer, intermediate and investment goods sectors.
In the first quarter, China's GDP grew 6.9 percent on-year, slightly faster than the 6.8 percent forecast in a Reuters poll and the fastest pace since the third quarter of 2015.
Data firm IHS Markit Monday said its Purchasing Managers Index for eurozone manufacturing-which is based on a survey of 3,000 companies-rose to 57.4 from 57.0 in May, reaching a 74-month high.
The pickup is consistent with other indications that economic growth in the currency area accelerated in the three months to June, having already speeded up in the first quarter.
A reading above 50 indicates growth, while that below denotes contraction in production.
"In many cases, businesses indicated that growth was held back as a reflection of water scarcity and the impending introduction of the goods and services tax (GST)".
The UK's manufacturing sector expanded at a slower rate in June than in the previous month, with rates of new business slowing down at home and overseas.
Nevertheless, overall confidence did weaken to a 7-month low as uncertainty surrounding the political outlook and Brexit talks increased once again.
But continued declines in energy prices, which weighed on manufacturing in Indonesia and Malaysia, could hurt these two economies, while in India, sluggish domestic demand offset strong foreign demand and led to a slowdown.
New orders expanded at the fastest pace in three months, boosting production and helping lift the PMI, Caixin said in a joint statement with data compiler IHS Markit.
An index measuring output, which feeds into a composite PMI due on Wednesday, jumped to 58.7 from 58.3 - a level not seen in over six years.