Lecturers went on strike this week in protest at the end of A-level courses at their college.
Union members at Cambridge regional college said teenagers from deprived backgrounds would be less likely to get to university, arguing that sixth-form colleges are too selective.
The Association of Teachers and Lecturers and the University and College Union held a one-day strike on Tuesday.
Chris Wilson, branch secretary of the ATL, said: "It's almost certain that cutting A-levels is going to impact on opportunities for students from deprived backgrounds unless sixth-form colleges radically change their mission and role in the community."
Students also say their student council funding was frozen after they tried to use it to pay for banners during their protest.
But the college says current students have been found alternative places at sixth-form colleges with better reputations for A-levels, although several have chosen to move to vocational courses.
Students will still be able to get access to higher education by doing one-year university foundation courses, the college argues.
Many colleges planning to cut A-levels say the recent Foster report has put them under pressure to focus more on vocational education and not to compete with sixth-form colleges and school sixth forms.
But Loraine Monk, from North East Surrey college of technology, where A-levels are also being cut, said its A-level students were more likely to be from ethnic minorities or from poor areas.
She said: "They come to college for another chance. They won't get that now. We are limiting the chances available, saying to these kids, don't go to university, they can do hairdressing and plumbing." Arranging for colleges to teach an entirely different curriculum from schools would also damage the lecturers' case for pay parity, she said.
North East Surrey, one of England's four failing colleges, justifies the cuts as part of measures to axe substandard courses.
Lubna Kazmi, director of student services, said its most deprived students were travelling from south London, often passing by other colleges which offer A-levels. There were also two sixth-form colleges in the area, she said.