The Council of Mortgage Lenders (CML) said £3.7 billion-worth of buy-to-let loans were handed out in January in total, increasing by 42% compared with January 2015.
While the bulk of buy-to-let borrowing in January was made up of remortgage loans, £1.4 billion was for house purchase, showing a 40% jump compared with January 2015.
The stamp duty hike was announced for buy-to-let landlords towards the end of 2015, and there have been signs of landlords rushing to complete purchases before the three percentage point increase on current stamp duty rates kicks in, on April 1.
The Royal Institution of Chartered Surveyors (Rics) has said surveyors are expecting to see a drop-off in sales of investment properties as the deadline for the hike approaches and investors no longer have time to complete sales before it starts.
But in the longer term, Rics still expects UK property values generally to increase by 25% over the next five years amid a lack of supply.
Rock-bottom interest rates have been keeping mortgage costs relatively cheap. The CML's figures also showed that home owners took out £5.8 billion-worth of remortgage loans in January, up 32% compared with the same period a year earlier.
Adrian Anderson, director of mortgage broker Anderson Harris, said: "Remortgaging and buy-to-let lending goes from strength to strength.
"More landlords are taking out mortgages and remortgaging as they try to buy before the stamp duty hike comes in from April, and are also looking at the costs associated with their investments, minimising their mortgage payments as much as possible."