Victoria University, based in the capital Kampala, opened in 2011 offering degrees from Buckingham it said would cost a fraction of the price of obtaining them in the UK.
But on 8 January the two institutions announced that they had suspended their partnership, leaving the future of around 200 students uncertain.
"We have both become increasingly concerned about the proposed legislation in Uganda on homosexuality and in particular the constraints on freedom of speech in this area," a Buckingham statement says.
A proposed anti-homosexuality bill, which has aroused international condemnation, would increase penalties for gay acts in Uganda.
The university was financed by Edulink, a Dubai-based company that helped establish Middlesex University's campus in Dubai.
Buckingham says it has "agreed to suspend our validation on the assurance that Edulink would produce viable arrangements for existing students on our validated courses to complete their studies".
Alistair Alcock, deputy vice-chancellor at Buckingham, said that one option would be for current students to join courses in the UK, although this would prove costly.
Many countries had anti-homosexuality laws, he said, but in Uganda "we're getting to the position where questioning whether there should be such legislation gets impossible".
According to a statement from Victoria, "under both UK and Ugandan law discrimination on a variety of grounds is prohibited; however there are fundamental differences between the two nations' respective laws regarding equality and diversity, which cannot be reconciled".