The problem is greatest for victims of violent crime, with a third going unrecorded. Of sexual offences, 26% are not recorded.
An HM Inspectorate of Constabulary report looked at more than 8,000 reports of crime in England and Wales.
The watchdog said the failure to record crime properly was "indefensible".
Home Secretary Theresa May described the findings as "utterly unacceptable", but police representatives said the situation had improved since the study.
The inspection reviewed reports of crime between November 2012 and October 2013 across all 43 forces in England and Wales.
It found that:
- Among the sample, 37 rape allegations were not recorded as a crime
- For 3,842 reported crimes, offenders were given a caution or a penalty notice - but inspectors believe 500 of those should have been charged or given a heavier penalty
- 3,246 of those offences that were recorded were then deemed to be "no crimes" - but inspectors believe 20% of those decisions were wrong and a crime had been committed
- The incidents recorded as "no-crimes" including 200 reports of rape and 250 of violent crime
by Danny Shaw, BBC home affairs correspondent
The under-recording of crime is more than a question of getting the statistics wrong.
If an offence isn't officially logged, it may not be investigated. And without a police inquiry there's no hope of finding the perpetrator and preventing other crimes.
Inspectors say there may well be people on the streets now, able to commit more crimes, who would have been locked up had their original offence been properly dealt with.
There are indications that some forces are improving. But there's also a warning in the report that increasing workload pressures among police - who are having to do more with considerably less - will "sharpen" the incentive not to record crimes.
"The position in the case of rape and other sexual offences is a matter of especially serious concern," said Chief Inspector of Constabulary Tom Winsor.
"It is particularly important that in cases as serious as rape, these shortcomings are put right as a matter of the greatest urgency. In some forces, action is already being taken in this respect."
He said the police should "immediately institutionalise" the presumption that the victim is to be believed.
"If evidence later comes to light which shows that no crime occurred, then the record should be corrected; that is how the system is supposed to work," he added.
'Lapses in leadership'
Police are obliged to inform victims about their decisions, but in more than 800 of the cases examined there was no record of the victim having been told.
Victims may have been under the impression that their crimes were being investigated when they were not, the report said.
It said relatively little firm evidence had been found of undue pressure being put on officers to manipulate figures.
But in a survey, some officers and staff did say performance and other pressures were distorting their crime-recording decisions, "and when presented with that picture, a number of forces admitted it".
Inspectors were told that pressure to hit crime reduction targets imposed by "middle managers" had the effect of limiting the number of crimes logged.
The report recommended that standard training established by the College of Policing be provided by each force.
'Pressures from workload'
Mrs May said: "It is never acceptable for the police to mis-record crime. Failing to do so not only lets down victims, but the wider public who expect to be able to trust the integrity of police recorded crime."
There had been "utterly unacceptable failings" in the way police forces have recorded crime but matters were improving, she said.
Shadow policing minister Jack Dromey said it was time for Mrs May to "get a grip on this and make urgent changes to the way the police record crime".
Chief Constable Jeff Farrar, lead for crime recording at the Association of Chief Police Officers, said: "Pressures from workload and target culture, use of professional judgment in the interests of victims, lack of understanding of recording rules or inadequate supervision can all lead to inaccurate crime recording.
"There have been allegations of improper practice, such as dishonest manipulation, in crime recording, however, the biggest and most in-depth inspection ever conducted by HMIC could not find anyone to come forward with any firm evidence to support this."
Ch Supt Irene Curtis, president of the Police Superintendents' Association, said recorded crime was a measure of demand on police resources rather than police performance.
"HMIC's report covers a period of at least 12 months ago and recognises that considerable improvements have already been made since that period," she said.
Earlier this year an interim report by Mr Winsor, covering 13 forces, made a similar conclusion that a fifth of crimes could be going unrecorded by police.
An unrecorded crime is classed as one that is reported to the police but not recorded as an offence.
Last month, official figures showed the number of rapes reported to and recorded by police in England and Wales was at its highest ever level.
The Office for National Statistics said there were 22,116 recorded rapes in the year to June, a rise of 29% on the year before.
Separate statistics from the Crime Survey for England and Wales showed overall crime fell by 16% to 7.1 million cases.
THIN BLUE LINE COMMENT
1.Nu Labour introduced performance targeting in 1997
2.Before this, the recorded crime & detection rate of the 43 forces had always been as you would expect, some good and some not-so-good.
3.Performance targeting rewarded Chief Officers with 15% bonus payments on top of their salaries.
4.Within 3 years (and for the first time in history) all but one of the 43 forces reflected massive decreases in recorded crime and increases in detections.
5.The dramatic downturn in recorded crime played a major part in the Coalition decision to include policing in the comprehensive spending review plan for cuts to the service that we have witnessed.
6.Crime rates play a large part of determining the resources required to police a force area.
7.Manipulated statistics lies at the very heart of what enabled politicians to use policing as a political football. "Crime has fallen dramatically" they said "so now we can deliver more with less".
9.The Chief Officers who were responsible, constructed, oversaw, turned an blind eye or allowed to continue the pernicious deceitful processes imposed upon the rank and file and the public.
10.The rank and file officers were compelled to implement policies that compromised their professional integrity.
11.The Public Affairs Select Committee, driven by the evidence of James Patrick and others revealed that recorded crime had been fiddled mercilessly for years. Chief Officers brought before the committee presented woefully, despicably defending the strategies they had either engineered or endorsed.
12. The Office of National Statistics withdrew its approval for police recorded crime, throwing official mistrust over the numbers.
13.Theresa May and others continued to adopt the "crime is falling because of our efforts" mantra.
14.It is no surprise that HMIC have found there is an "inexcusably poor" level of police recording of crime - with more than 800,000 crimes unrecorded each year.
15.It is also no surprise that the HMIC could only ever scratch the surface of the consequence of these practices. We would hardly expect there to be a paper trail of guilt ridden evidence leading the inspectors to uncover the whole spiders web mess that has been created.
16.When pointing the finger of blame for the malaise that exists within the service, yes, Theresa May, Tom Winsor Tony Blair and other notables have been instrumental.
17. The heaviest mantle of responsibility must lie with the Chief and senior officers, who, from 1997 onward, lacked the courage, vision and moral compass to resist performance targeting and the payment of divisive corruptive incentive bonuses. Only they benefitted. Everyone else, rank and file and the general public were cheated of the police service we deserve.
18.Chief Officers represent(ed) the service. If there had been more leaders and fewer managers, we might have seen a stronger resistance and rejection of performance targeting resulting in so much corruption and malpractice and decimation of morale.