The year is also likely to be the fourth-warmest ever for the world, which means that eight of the 10 hottest years recorded globally will have occurred this decade.
The figures reinforce the belief that global warming - the overheating of the atmosphere by industrial gases such as carbon dioxide - is significantly destabilising the climate.
"It is all consistent with what we think is happening, with the world warming up," said Professor Phil Jones, head of the Climatic Research Unit (CRU) at the University of East Anglia, Norwich.
Unless the rest of December is significantly cooler than forecast the last 12 months of the millennium will turn out to be Britain's hottest year by a tenth of a degree or more, said Professor Jones. It is expected to be 1.2C or possibly 1.3C above the recent long-term average. The previous record year, 1990, was 1.1 degrees above average.
"The intriguing thing is that little of the year has been outstandingly warm, but all the months apart from June have been above normal," Professor Jones said.
Britain's 10 hottest years so far, contained in the Central England Temperature Record maintained by the Met Office,are 1990, 1949, 1997, 1995, 1989, 1959, 1834, 1921, 1733 and 1779.
For the world, 1999 is continuing the rising trend of temperatures in the 1990s, the CRU figures show. It is likely to rank equal fourth with 1990, behind 1998 (the record), 1997 and 1995.