Some 40,104 mortgages got the go-ahead for house purchase in April, down from 43,854 in March when a "stamp duty spike" took place.
On April 1, stamp duty rates were increased by three percentage points for second home buyers, such as buy-to-let investors and estate agents previously reported dealing with a bottleneck of investors rushing to beat the deadline.
April's monthly mortgage approval total for house purchase is the lowest on the BBA's records since March 2015.
Dr Rebecca Harding, chief economic advisor at the BBA, said: "As expected, growth in mortgage lending has fallen back sharply on last month proving that March's results were just a stamp duty spike. Net mortgage borrowing is nevertheless 3% higher than a year ago."
The BBA's figures also show that deposits into Isas grew by £3 billion between March and April as the tax year drew to a close - less than half the £6.2 billion piled into Isas during the same period in 2015.
Savings rules were changed on April 6, with the introduction of the personal savings allowance. The allowance means a basic rate taxpayer can earn up to £1,000 in savings interest tax-free, while a higher rate taxpayer can to earn up to £500 tax-free. Money held in Isas does not count towards the new personal savings allowance. Traditionally, people have used Isas to ring-fence any interest they earn on their cash pots from the taxman, but the new allowance has taken most people out of paying any tax on their savings interest altogether.
The BBA's figures also showed that personal deposits generally grew by 4.8% annually in April.
Dr Harding continued: "The fact that personal deposits are growing while Isa deposits continue to under-perform suggests consumers are using easy-access savings while the outlook for the economy remains uncertain.
"The increase in real wage growth may start to have positive knock-on effects on long-term savings if it is sustained."
The BBA also said borrowing by non-financial companies increased by £300 million in April, following similar growth in March and marking the fourth month in a row to show an increase.
Some housing market reports have suggested the stamp duty increase meant house purchases that might otherwise have taken place later in 2016 were brought forward to early 2016.
Howard Archer, chief UK and European economist at IHS Global Insight, said: "The strong suspicion is that housing market activity will be pressurised in the immediate term by a combination of weakened interest from the buy-to-let and second home sectors as well as heightened concerns and uncertainties over the UK economic outlook, particularly in the run-up to June's referendum on EU membership."