In the last month, prices went up by 1.7%, said the Halifax, bringing the average price of a home to £208,286.
However, other lenders, such as the Nationwide measure, put the rate of increase much lower.
Last month, it said prices rose by 4.5% in 2015, less than half the Halifax estimate.
Halifax’s housing economist, Martin Ellis, said one reason for the sharp increase was the continuing shortage of property for sale.
“This situation is unlikely to change significantly in the short term, resulting in continuing upward pressure on prices,” he said.
The last time UK house prices rose so quickly was in 2006, when values soared by 9.9%.
The 9.5% increase in 2015 was way ahead of experts’ predictions a year ago.
Martin Ellis himself predicted that prices would rise by between 3% and 5%, while most expected a figure around 4%.
Newham, in East London, was the town with the largest increase in 2015. Prices there rose by 22% in 2015, compared to 12% for London as a whole.
The different methodology of the most popular house price measures is explainedhere.