But the study, Mapping Provision, carried out for the Further Education Funding Council, estimated that demand from people with disabilities or learning difficulties could be double that figure.
Some 63 per cent of colleges surveyed admitted having turned away some students with special needs. But even more said they could not estimate the level of demand from people who had not tried to get on a course.
Researchers said colleges relied on ad hoc information about local communities and needed to do more to assess demand for education. They said: "It is clearly very common, for example, to use information from local schools, education authorities and health authorities to assess potential demand.
"There was no evidence from the survey, however, that colleges had been able to integrate data from these different sources to build up a systematic picture of their local catchment areas."
The survey of 274 colleges found wide variations in the number of special needs students taught by each institution. Agriculture and horticulture colleges had the highest percentage of people with disabilities and learning difficulties, with the rest split between art and design, tertiary, sixth-form and general FE colleges.
The vast majority (90 per cent) tried to identify students with learning difficulties, but as many as 44 per cent of colleges said they believed they had students with unidentified special needs. Thirty per cent of colleges said there were enrolled students with special needs which could not be met because of staffing problems or physical obstacles.
The report comes four months after the Tomlinson committee on special needs in FE concluded that disabled students get a poor deal in colleges, although the sector is meeting its legal obligations.
The committee recommended a Pounds 5 million staff development programme in FE and a tough new inspection framework paying greater attention to colleges' track record on matching teaching to the learning needs of all students.
The 50 recommendations in Professor John Tomlinson's report included suggestions that colleges should collaborate with regional bodies to focus more clearly on special needs when drawing up strategic plans.