The study follows research published by the agency which suggests that colleges giving help with reading, writing and maths have lower drop-out rates.
Alan Wells, director of the BSA, said the student profile was radically different from a decade ago with a sizeable percentage needing help with basic skills .
"This isn't necessarily a sign that standards are deteriorating, more a tribute to the colleges' powers of persuasion and an increasing recognition of the advantages of further education," he said.
The 18-month study carried out by the University of Central England and Bilston Community College found that most colleges screened full-time students to see if they needed support, but very few screened part-timers. Almost a third needed help and two-thirds got it.
"Students identified as needing basic skills support were more likely to stay at college, complete their courses and achieve qualifications if they received support than if they did not," said the report. It also found that students taking general national vocational qualifications were more likely to drop out.
The BSA is concerned about the number of colleges which failed to trace students needing extra help.