Ministers have been urged to “get a grip” of so-called gagging orders that have seen millions of pounds handed to government staff.
The National Audit Office condemned the lack of “transparency, consistency and accountability” around the compromise agreements - which can mean individuals are paid additional sums to leave organisations quietly.
The criticism came in a report by the public spending watchdog following widespread concern about the controversial deals.
There are claims that health service executives have been prevented from speaking out about poor care in hospitals.
Local councils are also reported to have distributed hundreds of millions as a result of compromise agreements, while the BBC paid out £28m over the past eight years.
According to the NAO, the Treasury has signed off more than 1,000 special severance payments linked to compromise agreements since March 2010 - worth a total of around £28.4m.
But the true figure is likely to be much higher as comprehensive records are not kept, and decisions are sometimes made by departments or through judicial mediation.
The watchdog found that 49 out of a sample of 50 cases included a confidentiality clause covering the existence and terms of the agreement.
The auditors stressed that there were legitimate reasons for such deals, including protecting intellectual property or resolving grievances.
None of those it looked at would have legally blocked an individual from whistleblowing.
“However, some people we spoke to who had been offered, or accepted, compromise agreements have felt gagged,” the report added. “An organisation’s culture, the events leading up to the person being offered an agreement, and the wording of the agreements contributed to whether the individual felt gagged.
“Legal advice to the employee is a prerequisite of making a compromise agreement legally enforceable.
“However, the individuals we spoke to felt that it was not generally made clear that confidentiality clauses do not prevent employees from raising legitimate public interest concerns.”
The report found the Treasury had approved £11.1m in special severance payments by the Department of Health in the three years to March. The highest was £266,000.
One Ministry of Justice pay-off was recorded as £250,000, while the top figures at the Home Office and Department for Education were £225,000.
The actual amounts might have been lower depending on final negotiations with the individual.
Neither the Cabinet Office nor the Treasury provide formal guidance to departments on use of compromise agreements.
The Treasury has indicated it does not believe there is any need to collect data on the deals centrally, according to the watchdog.
NAO head Amyas Morse said: “Compromise agreements are widely, and often legitimately used.
“But the lack of transparency, consistency and accountability is unacceptable.
“With the public purse under sustained pressure and services increasingly delivered at arm’s length, it is important that compromise agreements do not leave staff feeling gagged or reward the failure either of an employee or an organisation.
“The centre of government should get a grip on the use of compromise agreements in the public sector.”
Public Accounts Committee chairman Margaret Hodge said: “It is staggering that no one has any idea how many compromise agreements are used and whether, overall, they are value for money.”
The Labour MP went on: “The Treasury looks at cases individually, so it can’t say where most applications come from, what the total sums involved are or how much of the amounts it approves are paid by departments, following negotiations.
“Even within departments central records are rare. This total absence of oversight means the figures approved may be just the tip of the iceberg.
“No-one has any idea if departments use these agreements excessively to reward failure or avoid unwelcome publicity.
“Similarly no one knows whether individuals abuse them by moving around to hide poor performance, picking up payments as they go.
“Payments may be lower on average and included in contracts, but there are individual cases where obscene amounts have been approved; as much as £266,000 in the Department of Health and £120,000 in the Ministry of Defence.”