The CBI Industrial Trends Survey showed the balance of firms that increased their total orders rose to minus 7, an improvement from minus 11 last month and minus 18 in October.
The report said overall production volumes edged down to minus 3 in December from plus 4 a month ago, and firms expect output to decline further over the coming three months.
Motor vehicles, aerospace and transport equipment were the greatest contributors to order books, while mechanical engineering lagged.
For the second month in a row companies also expect selling prices to be broadly flat over the coming quarter.
Rain Newton-Smith, director of economics at the CBI, said: "Manufacturers are still having a tough time of it with output slipping and exports remaining a weak spot in spite of an improvement at the end of the year.
"But there is a pick-up in orders from previous months which could be a sign of light at the end of the tunnel."