Campaigners warned 20,000 inmates are sharing cells designed for fewer occupants after a sharp jump in the jail population over the last 20 years.
The three most overcrowded prisons have the second worst of four performance ratings, according to analysis of Ministry of Justice data carried out by the Prison Reform Trust.
And five of the six jails whose performance is described as being “of serious concern” - the lowest rating - are overcrowded, the study said.
HMP Leeds was identified in the analysis as the most overcrowded prison in England and Wales. Designed for 669 men, as of October the prison held 1,145.
Leeds was followed by HMP Swansea (built for 268, holding 456) and HMP Wandsworth (built for 943, holding 1,564). All three were rated as “of concern” in the MoJ’s annual performance report for 2015/16.
The report found that half of the 30 most overcrowded prisons have the lowest or second lowest performance grading.
This proportion was almost twice as high as that seen across the estate. Of the 117 establishments in total, 31 have a performance that is “of concern” or “serious concern”.
Only one of the eight prisons rated as having “exceptional performance” is overcrowded, the paper added.
The Prison Reform Trust said overcrowding “cripples the system’s ability to provide a decent and constructive public service”.
Peter Dawson, director of the charity, said: “The bleak state of our prisons is a political failure, shared by all governments of the last two and a half decades.
“Three years of austerity have now brutally exposed the system’s inherent vulnerability, and a comprehensive strategy to control the demand for prison, and so to end overcrowding, must form part of this government’s response.”
The prison population - which currently stands at around 85,000 - has come under the spotlight in the wake of the jail safety crisis sparked by surging levels of violence and self-harm behind bars.
Last month former justice secretary Michael Gove warned that too many people are being sent to prison, while the Lord Chief Justice has emphasised the need for tough alternatives to jail.
Michael Spurr, the chief executive of the National Offender Management Service, told MPs last week that around 24% of inmates are held in accommodation designed for fewer people than are in it. This is either a single cell with two prisoners, or a double cell with three inmates in it.
Mr Spurr warned that a point where cells are only holding the number of prisoners they were designed for would not be reached within this parliament or the next.
The Government’s prisons overhaul aims to create a less crowded estate, including a £1.3 billion programme to build up to 10,000 new adult places.
A Ministry of Justice spokeswoman said: “The Justice Secretary has been clear that our prisons are in need of reform.
“We are investing £1.3 billion to build modern new establishments, with 10,000 new prison places and better education facilities.
“Along with our plans set out in the Prison Safety Reform White Paper, this will help give offenders the skills they need to turn their lives around.”