Professional industry bodies have voiced their fears in a letter to Davis as he leads post-referendum negotiations.
They believe major construction projects will be at risk and “Britain could stop building”.
The warning comes from The Royal Institution of Chartered Surveyors, the Royal Institute of British Architects, the Chartered Institute of Building and the Royal Town Planning Institute.
The letter states: “There is a real concern within our industry that if access to a skilled workforce is further restricted, Britain could stop building.
“We therefore urge the Government to explore options and approaches to ensure that this access is not impeded to the detriment of the built environment.”
The group is also urging the Government to step-up public investment.
It said: “Providing confidence to the construction industry through infrastructure funding and development will provide stability during a period of uncertainty and ensure that the UK is well-placed to take advantage of growth opportunities in the future.”