The CIPS index, which measures overall activity, registered just 29.3 for December.
The figure – well below the growth mark of 50 – is the weakest seen since the survey began in April 1997.
CIPS director of professional practice Roy Ayliffe said payrolls had been cut for the seventh consecutive month as firms axed staff.
He also warned over further pressures on the sector in the year to come.
Mr Ayliffe said: "The New Year spirit was decidedly muted among UK constructors amid reports of ever toughening market conditions - further falls in global demand resulted in the most severe retrenchment in the [index’s] 11-year history.
"Amidst a climate of doom and gloom, firms were forced to axe more jobs in preparation for what is set to be another year of trouble and turmoil."
CIPS said the level of new orders placed with UK contractors also fell at the fastest rate on record last month.