Ofsted visited six Schools Partnership Trust (SPTA) academies as part of routine inspections and found five were not offering good quality education.
One school retained its "inadequate" rating by Ofsted.
SPTA accepted improvement was needed but said there was "ample evidence" it was "an effective" academy sponsor.
The judgements are significant because putting poor performing schools under the leadership of non-profit-making academy trusts or sponsors is the government's key engine of school improvement.
Sir Paul Edwards, chief executive of SPTA - which runs 44 schools in the Yorkshire and Humber area, has also worked as a government adviser in the Department for Education's academy and free school programme.
'Ill-prepared'
England's education inspectorate is not allowed to inspect academy chains in the same way as it inspects local education authorities.
Ofsted inspected the six schools over a 10-day period in June and sought further information on how SPTA has been performing on school improvement.
It said concerns had been raised about how well it was performing.
Four of the academies still required improvement, Ofsted said, although two of these had begun to improve.
One academy remained inadequate, but a sixth had improved to "good" from its previous rating of "satisfactory".
The inspections also highlighted key weaknesses in the schools, such as inconsistent teaching that does not challenge pupils enough and low standards at the end of primary school. This meant too many pupils had been ill-prepared for secondary schools, Ofsted said.
It also said governors lacked expertise to challenge senior leaders on teaching quality.
But inspectors added that most of the principals it contacted felt they were well supported by trust officers and that SPTA human resource departments had assisted in managing under-performing staff.
In a letter to Sir Paul, Ofsted said: "In summary, there is some evidence of effective school improvement, particularly in the initial start-up period after conversion to academy status. However, the quality and impact of governance arrangements are variable.
"There are further concerns regarding the depth and accuracy of SPTA analysis of data showing pupils' progress and the contribution this makes to rapid school improvement.
"Above all, there are too many underperforming academies which have remained in this position for too long."
An SPTA spokesman said the trust recognised the important role Ofsted had played in monitoring standards in the school system.
"The trust also recognises that Ofsted comments around areas for improvement are suggested on the basis of constructive dialogue to ensure all children receive a first class education, regardless of the school setting," he said.
"Equally however, the trust also recognises that the evidence to support these comments was largely drawn from a small sample of six schools, in a multi-academy trust that supports in excess of 42 schools and which contains two Teaching Schools, accredited through the National College of School Leadership.
"Whilst the trust looks forward to discussions with Ofsted about how to improve our performance, it is important to consider the facts in relation to the whole group, not just the six schools that were inspected."
SPTA is the third chain to be criticised by Ofsted, with critical letters recently sent to both the Kemnal Academies Trust (TKAT) and the E-ACT Trust - one of England's biggest academy organisations.
An academies trust led by a former government adviser has been told too many of its schools are underperforming and not improving fast enough.