Its annual ratings show 28 out of 126 jails, including the three opened under the coalition government, are “of concern” – the third of four ratings.
Only one – Brinsford Young Offenders Institution in Wolverhampton – got the lowest “of serious concern” rating.
Justice Secretary Chris Grayling said prisons “are still running safe and decent regimes”.
The prisons opened under the current government are Oakwood in the West Midlands and Thameside and Isis, both in south London.
Oakwood and Thameside both opened in spring 2012 and are privately operated.
Isis, a publicly-run jail for adults and young offenders in south London, opened in July 2010.
The ratings come from the National Offender Management Service, an executive agency of the Ministry of Justice.
Its Prison Rating System (PRS) lists performance in four categories: public protection, reducing reoffending, decency and resource management and operational effectiveness.
Overall performance is graded into one of four bands.
These bands are – 4: exceptional performance, 3: meeting majority of targets, 2: overall performance is of concern, and 1: overall performance is of serious concern.
Separate figures show the number of prisoners who died in custody in 2013-14 was 225 – up from 181 in the previous year and higher than in any of the previous nine years.
The figures in the report only go back to 2004-05, but the next-highest figure in that period was 211 in 2011-12.
Of the 2013-14 deaths, 88 were recorded as self-inflicted, 127 were from natural causes, three were homicides and seven were listed as “other”.
Speaking about the number of deaths, justice minister Andrew Selous said the government was “working hard to understand the reasons for the recent increase”.
“But this is a complex issue and there is no simple explanation, with the prison population containing a high proportion of very vulnerable individuals,” he said.
Mark Leech, editor of the national prisons newspaper Converse said Chris Grayling was “ignoring the facts”.
Mr Leech said: “We’ve been warning Grayling for the last two years that his policies of savage budget cuts would have devastating effects and, now they are, he is choosing to ignore the facts when all the evidence is overwhelming.
“You cannot strip half a billion pounds from prison service budgets and expect it to carry on as if nothing has happened – all the more so at a time of record overcrowding and a massive shortage of staff – its sheer lunacy to expect that nothing will give – of course it will, and it is doing.”