The survey, from the Confederation of British Industry, also shows year-on-year sales growth in the first half of this month has fallen short of retailers' own expectations.
Anna Leach, the CBI's head of economic analysis, said: "This month's survey hasn't quite provided the Christmas cheer that retailers anticipated, with sales growth falling short of expectations."
She added: "Clearly, weak spending power and uncertainty over the economic outlook are likely to remain key risks to the retail sector in 2013."
Of the retailers surveyed by the CBI between November 29 and December 12, 36% reported that sales volumes in December were up on a year earlier and 17% said they were lower.
Although the resultant balance of 19% declaring a year-on-year rise in sales was only just adrift of the long-run survey average of a net 21% reporting such a position, it was down sharply from a corresponding figure of 33% in the CBI's November distributive trades survey.
And, in the November survey, a balance of 25% of UK retailers had predicted their December sales would be higher than a year earlier.
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "The CBI distributive trades survey for December was weaker than expected, fuelling concerns that retail sales are lacklustre so far over the vital Christmas period. This is particularly worrying news for retailers, and it does not do much for overall growth hopes for the fourth quarter."
However, Mr Archer emphasised that the performance of retail sales in early December, signalled by the CBI survey, was "not disastrous".
Only a net 10% of retailers surveyed by the CBI expected sales volumes in January to show a year-on-year rise, signalling their confidence has dwindled in the past month.
Martin Beck, UK economist at consultancy Capital Economics, said: " December's CBI distributive trades survey suggested that activity in the festive shopping period is proceeding at a pretty modest pace. Retailers will be hoping the last few shopping days before Christmas see a resurgence on the high street."
He added: "On the basis of past form, December's number is consistent with annual growth of the official measure of retail sales volumes of close to 4%.
"Nonetheless, the CBI survey has tended to present a stronger picture than that presented by the official data. And the survey indicated a more pessimistic outlook among retailers."
Mr Archer said: "Retailers will be fervently hoping there is a strong final rush in sales over the final days before Christmas and that many consumers are leaving their present-buying until the last moment."
The CBI survey showed particular strength in the grocery, clothing, and furniture and carpets sub-sectors in early December. However, sales of durable household goods and recreational goods were particularly weak.
The value of retail sales north of the Border in November was down 1.2% on a year earlier, according to a survey published earlier this month by the Scottish Retail Consortium. The SRC survey also signalled the retail sector remains significantly weaker in Scotland than in other parts of the UK.
The November figures for Scotland were even more disappointing, given that the value of retail sales north of the Border in November last year had been down 1.3% on the same month of 2010.