The colleges say that the number of pupils joining them halfway through their two-year A-level courses has risen sharply since the introduction of league tables four years ago.
Many of the pupils are from independent schools but some state schools are also pressing candidates to withdraw from A-level subjects in the middle of their courses. Schools deny that pupils are being forced out because of league tables but Elizabeth Rickards, principal of Davies Laing and Dick, a London tutorial college, said: "The number of students coming into our upper sixth has risen from zero to 20.
"This is market forces gone mad. Some schools are being absolutely ruthless... It costs pounds 8,190 to do three A-levels here. What worries me is what happens to the pupils who cannot afford to come here."
Last week, Ms Rickards saw a pupil on an assisted place at an independent school who had been told she could not continue there because she was likely to fail maths.
Charlotte Gilliam, another pupil, who attended the fee- paying Queen's College, in Harley Street, London, until March this year, was told just three months before she was due to take her A-levels in maths, physics and geography that she had to stay on another year if she wanted to take them. She had failed her maths mock exam and several resits.
Kate Gilliam, her mother, said: "It was like a thunderbolt. We asked if she could at least take her geography and physics. They said `no'. Charlotte asked if it was to do with league tables but they said it was school policy. She went to a tutorial college but I wasn't surprised that she failed her A- levels. She was so devastated to have to leave."
Alexander Burlak, whose daughter, Alexandra, attended Joseph Rowntree School in York, a comprehensive, said she was "heavily pressured not to enter A-level biology halfway through the course. I protested and they eventually agreed to let her take it. She got an E [the lowest pass grade] and is now about to start her third year at university studying marine biology. She was told by the school she might fail and if she failed it would affect the pass rate. In every other way it was an excellent school. The pressures on schools are grossly unfair."
Another father who did not wish to be named said his son had been forced off an A-level course at a single-sex grant maintained school. The school made him pay his own exam fee so they did not have to include him in the league tables.
Lady Goodhart, principal of Queen's College, said it was her school's policy that everyone should take three A-levels and that everyone knew that if they failed their mock exams they were unlikely to be allowed to take the A-level.
"If I were in the horse world, I would not put horses over hurdles they could not jump," she said. "... In the case of Charlotte Gilliam the only thing I feel we can be criticised for is waiting for so long before we asked her to take another year."
Dr David Selby, the new deputy head of Joseph Rowntree school, said he would not comment on the case of Alexandra Burlak which happened before he arrived. But he added: "The only criterion we use is the students' best interests. If someone were doing disastrously it would not be fair to let them carry on." The school was very confident of its predictions about A-level performance based on GCSE results. It made a commitment to teach students to A-level and it would be very rare for someone to be asked not to take the exam, even if they were borderline.