Some 80,285 mortgages with a collective value of £13.6 billion got the go-ahead in January - marking a jump of one third (33%) compared with January 2015, the British Bankers' Association (BBA) said.
It is the first time since January 2014 that mortgage approvals have edged above the 80,000 mark in a single month.
From April 1, people buying additional properties, such as buy-to-let properties and second homes, will pay an extra three percentage points above current stamp duty rates.
The BBA's figures showed that 47,509 mortgages worth £8.6 billion in total were approved for house purchase in January, marking a 27% increase on the same period a year earlier.
And re-mortgage approvals were up by 42% on a year earlier, with 25,040 home loans worth £4.5 billion collectively getting the green light in January.
Richard Woolhouse, chief economist at the BBA, said: "The start of the year has seen a significant rise in mortgage borrowing.
"It seems that this has been driven, in part, by borrowers looking to get ahead of the increases in stamp duty for buy-to-let and second home buyers scheduled to come into effect in April."
The continued availability of cheap mortgage deals - and households' fading expectations that interest rates will start to increase any time soon - are also thought to have been boosting the housing market.
Financial information website Moneyfacts.co.uk reported this week that the choice of mortgage deals for people with low deposits is at its widest since 2008, with 845 products on the market for people with deposits of 5% or 10% across the UK.
The average two-year fixed-rate mortgage now on offer for someone with a 10% deposit has fallen below 3% for the first time on Moneyfacts.co.uk's records, which go back 26 years.
The BBA also said that borrowing by non-financial companies increased "fairly strongly" in January, after declining in December, with a £3.4 billion upswing recorded in January.
Mr Woolhouse continued: "Net lending to non-financial companies saw the biggest monthly jump since July 2008 as businesses take advantage of record low interest rates. Demand from the transport, storage and communication and construction sectors was particularly strong."