The FPC has recommended that only 15% of the total of all residential mortgages should be available at or above 4.5 times a borrowers' income.
But in its response to the FPC's consultation, the BSA raises concerns about the extent to which the higher loan to income cap will impact younger buyers in particular.
It said the proposal reduces the ability of individuals to get on the property ladder, meaning that people may not be able to buy until they are much older.
Robin Fieth, chief executive of the BSA, said: "This is the first time that macro-prudential tools have been used to control the housing market and the actual effects are an unknown quantity.
“Of course, affordability is crucial and banks and building societies should only lend what a customer can reasonably repay, however our concern is the effect these measures will have on first time buyers in and around the capital."
In the next 12 months, up to 20 building societies will be affected by these measures but lending by building societies at LTI's of 4.5 times or more has been low this year to date, accounting for under 7% of all lending.
However in its submission, the BSA recommends that smaller lenders with gross mortgage originations between £100-£500m have a higher LTI limit based on a fixed number of loans rather than 15% of overall lending to ensure the first time buyers are still able to get a mortgage that meets their needs.
