HMRC said there were 64,490 completed sales during January compared to 60,530 in January 2012.
The figures also reveal a 0.05% increase in property transactions between December 2012 and January 2013.
Ben Thompson, managing director of the Legal & General Mortgage Club, said: “The data from the HMRC today is another indication that we are right to be cautiously optimistic about a recovery in the housing market especially as it reveals a 3% increase in residential transactions on the same period last year.
“While constraints on credit do remain and we expect the volume of transactions to remain broadly flat over the course of 2013 things are slowly starting to claw their way back to something approaching ‘normality.’
“Our hope is that lenders will be seeking to do more business this year and that we will begin to see an upward and sustained momentum that will start to take us towards a healthier housing market overall.”