The Adult Learning Inspectorate found that services in Hackney, east London, described in 2003 as "inadequate", were now at least satisfactory.
Teaching is satisfactory in 93 per cent of lessons, compared to just 79 per cent two years ago, after the trust addressed concerns about some of the small community groups which run courses.
Trish Smith, head of adult and community learning, said: "The 2003 report was a bit of a wake-up call. It's much, much more professional now."
The trust was the first not-for-profit company to run an entire council education service when it took over in August 2002 from the private firm Nord Anglia, which had failed to deliver improvement.
Stricter quality control was introduced and the trust hired its own teachers to support unqualified staff running community courses. The trust's leadership was praised for increasing recruitment of students, ethnic minorities and older learners.
It was given a satisfactory rating for hospitality, sport, leisure and travel, which were all previously unsatisfactory.
Its most popular courses, in visual and performing arts and media, are now judged to be providing a good service for the 2,600 learners.
Family learning programmes have also been given a clean bill of health after being rated as very weak two years ago.
But foreign languages courses and higher-level English courses were axed after they were rated very weak two years ago.
In 2003, inspectors found that attendance and punctuality were poor on many courses, with latecomers disrupting the lessons.
They said it had improved on most courses, increasing from 50 per cent attendance to 74 per cent in one example, although, on foundation courses, both staff and learners arrive late.
Hackney had been ordered by the Government to bring in a private provider to manage the local education authority after years of failure under the "malign influence" of the council.
The trust, led by a board of directors including headteachers and school governors, has a 10-year contract to run the borough's schools, nurseries, and the adult education service.