The Information Commissioner has threatened the Cabinet Office and the Ministry of Defence with regulatory action, after the departments failed to sufficiently cut the time they take to respond to Freedom of Information requests.
Christopher Graham said he had "particular concerns" about the departments, as well as Birmingham City Council, which was also failing to cut its FOI response times sufficiently.
A number of local councils have also been told to sign undertakings to improve their performance, including Wolverhampton, Islington and Westminster.
The Home Office, the Metropolitan Police Service, NHS North West, the London Borough of Croydon, the Scotland Office and the London Borough of Newham have also been informed that there are "some areas of concern" in their FOI responses, even though they are meeting the required standard.
The warnings come after the Information Commissioner's Office monitored 33 public authorities over three months. The remaining 26 authorities have maintained or improved their response times "sufficiently", Graham said, and no action is being taken against them.
"Responding promptly to FOI requests is key to delivering citizens' rights," he added. "Too many public authorities are taking too long to decide either way whether to release information or to refuse requests."
Graham said the ICO is set to monitor 18 other public organisations over the next three months to evaluate their performance. They include Barnsley, Cornwall, Kingston and Surrey councils, as well as the City of London Police, Surrey Police, the Department for Education, East Lancashire NHS Trust, the Equality and Human Rights Commission and the Highways Agency.