The Quality Assurance Agency scheme was launched earlier this month to enable institutions to use the body's logo in marketing material to help reassure students over academic standards.
Any university receiving a positive judgement in institutional-level reviews conducted by the QAA can use the mark.
However, four institutions - Trinity Laban Conservatoire of Music and Dance, the University of Bradford, Leeds Metropolitan University and York St John University - cannot use it because they received limited-confidence judgements in their most recent inspection.
Liverpool John Moores University has also been refused permission to adopt the logo after aspects of its overseas collaborative provision were criticised (although domestic teaching met sector guidelines).
University Campus Suffolk and Leeds College of Art, which have both yet to receive a full institutional review, will also have to wait to use the quality mark.
The most recent of the negative-review judgements was made against Trinity Laban, which has been told that it needs to improve its learning opportunities to meet UK expectations.
According to an institutional review published last month, action is needed to address students' concerns that written work is not marked on time and that some feedback is too brief and sometimes illegible.
Timetables are not always available for first-year students, limiting subject choice, while support for postgraduate research students is also deficient in some areas, the report adds.
However, the South London conservatoire - formed in 2005 through the merger of the Trinity College of Music and the dance school Laban - met expectations for academic standards and had several exemplary aspects of good practice, the QAA review found.
Anthony Bowne, principal of Trinity Laban, whose degrees are validated by City University London, said the review showed the institution was "organically sound".
"This particular review is unusual in that it was conducted two years earlier than required, at our request, to help us take stock of the merger of our two heritage colleges and to prepare for a future taught degree-awarding powers application," he added.
Institutions with limited-confidence judgements can still go on to use the QAA's quality mark if they take the action deemed necessary by the body.