Last month's reading on the PMI was 54.1 - down from June's level of 58.4 - but there are still indications of strength in the industry, the report said.
For the fifth consecutive month, UK construction companies noted a rise in new orders, which supported the growth of the sector.
David Noble, chief executive officer at the CIPS, commented: "We're finally starting to see the growth in activity tail-off and normalise at a slightly slower rate"
Residential house building was the most successful sub-sector in July, while commercial work expanded at a quicker pace than civil engineering.
This comes after James Roberts, head of real estate consultancy Knight Frank, said that there would be a recovery in the private property market, with lower demand for the assets simply a "pause for breath".
Posted by Jonathon Gordon