This follows the publication three weeks ago of the report on the first failing college, Charlotte Mason, and will heighten anxiety about the quality of teacher training.
An anonymous letter from the college claims that the inspectors found quality assurance and management at La Sainte Union HE College were inadequate and that this was adversely affecting the content and quality of education in the three other areas that OFSTED considers - English, maths, and assessment.
Inspections took place in November and again in February, and the college is due to receive a draft copy of the final report in the next few days.
The leaked correspondence includes a memo from the principal, Anand Chitnis, in which he describes inspectors' comments after the first visit, explaining that quality assurance had been marked "unsatisfactory" (grade 4) and the other areas "sound" (grade 3, which OFSTED interprets as "in need of improvement").
Problems included, writes Mr Chitnis, "lack of coherence in education programmes and specific subject provision", "absence of staff development", and "absence of auditing student skills".
Also included in the package sent to The TES were minutes from an emergency meeting of the staff council in which staff express extreme dissatisfaction with management, and complain of low staff morale due to "anxiety about the future of the college".
Mr Chitnis is described as "autocratic, secretive and intimidatory". The inspection had been "compromised by lack of leadership" and the BEd course is "precarious", say the staff.
John Layman, the assistant principal, asked to comment on the leaked documents, was anxious to emphasise that the college had already begun extensive reorganisation of the management structure and that "feathers may have been ruffled in the process". There had been no redundancies, he said. Staff had been redeployed in order to bring all the initial teacher training (ITT) tutors under one roof.
He said that it was unwise to pre-empt the final report. "Let us hope that the inspectors recognise what has been done - moves were under way well before the return visit."
An OFSTED spokesman confirmed that a report on the Southampton college was due in June. Almost half of the 68 institutions being inspected in OFSTED's sweep of primary ITT have now been visited, and nine reports have been published.