Elderly care charities said the "appalling" findings of the investigation laid bare the lack of regulation in the social care industry.
Recent figures show that 543,000 adults in England receive home care through their local council with another 150,000 paying for it privately. There are thought to be about 800,000 more seeking care.
The cases came to light after an investigation for a BBC Inside Out documentary in the West Midlands, prompted by the death of an elderly woman who was allegedly left untended at home for long periods.
The investigation into standards in private care agencies found that 13 operators in the region had employed convicted criminals and eight others had not been checking the records.
All of them are still operating despite concerns being raised by the health watchdog, the Care Quality Commission (CQC).
The programme found that more than 500 allegations of abuse or poor practice had been made to authorities in the area in the past year.
Further inquiries by The Daily Telegraph found examples of criminals employed as carers in the homes of vulnerable elderly people across the country as well as staff allowed to work without criminal record checks or before the checks were finished.
More than 220 care agencies working in elderly people's homes in England have failed to show they were employing properly qualified and vetted staff in recent CQC inspections.
There are fears this could be the tip of an iceberg. Not all agency records on vetting staff are checked at each inspection.
Fewer than two thirds of the 6,000 agencies have been inspected by the watchdog, set up four years ago.
"People are going to be shocked and horrified because people have an expectation in the social care system and regulation that isn't true," said Gary Fitzgerald, chief executive of the charity Action on Elder Abuse.
"People have a false faith that we have a system of providing social care that in general can be guaranteed - but it isn't."
More than 6,000 private care agencies are working in the homes of elderly people across England. Many of them are working on contracts for local councils, which are under pressure to slash their budgets and find the best "value" for taxpayers.
The investigation was launched after concerns raised by Peter Taylor, a Birmingham electrician, about the care provided to his mother, Dorothy, 87, who died last year. His complaints about Care 4 U, an agency based in the Perry Barr area of Birmingham, triggered inspections that uncovered a series of failings.
The agency was found to have employed 23 people with convictions for crimes including theft, assault and handling drugs.
"If I hadn't gone and requested an inquest none of this would have come to light," said Mr Taylor.
Even after failings were uncovered, the agency retains its £800,000-a-year contract with Birmingham City Council and is licensed by the CQC.
"I'm appalled at the CQC," said Mr Taylor. "They found all these things wrong but do nothing about it."
CQC inspection reports show similar failings in agencies across the country which are still in operation.
Last year the watchdog received a tip-off that staff at an agency in Sussex, were being allowed to work before criminal records checks were completed.
Subsequent inspections found that a string of employees had convictions - including one with 12 serious offences.
Last March, inspectors at Calderdale Home Care Associates in Halifax were told that most of the criminal checks had been discarded.
Those that were available contained details of staff with criminal convictions and one employee had been referred to the Home Office by a previous employer.
When inspectors went to an agency in Essex last June they found paperwork detailing two criminal convictions on a table but were assured that it was "all right as the person … had left".
Neil Duncan-Jordan, of the National Pensioners' Convention, said: "This should be a massive wake-up call to both the Government and the CQC to sharpen up its procedures.
"The CQC seems incapable of doing the job that the public thinks that it is doing because it is reactive, it goes in after the problems have been identified. That is not good enough. If they are not able to do more, then we need another agency that will." Dr Ros Altmann, the director general of Saga, said it was "shocking" that care workers could ever be allowed to work without proper criminal records checks.
"It is unacceptable that the social care system in this country has not been taken seriously enough," she said. "We are talking about people's lives."
A spokesman for the CQC said: "Having a criminal conviction does not in itself prevent a person from working in health or social care.
"If a criminal records check discloses a conviction or other relevant information, the employer has to decide whether the person is suitable to be employed."
A spokesman for Birmingham City Council said problems with Care 4 U in Perry Barr were identified and further work was suspended. "Improvements have now been made," he said.
A Department of Health spokesman said the CQC was able to intervene to raise standards. The watchdog was "working with Care 4 U to ensure improvements continue to be made", he said.
BBC Inside Out West Midlands can be seen on BBC One tonight at 7.30pm and on BBC iPlayer all week.
