The watchdog is also concerned over Met police’s failures to respond in time to information requests.
The Information Commissioner’s Office (ICO) has put four English local councils under watch for their sub-standard response times to requests for information.
The London Borough of Lambeth, the London Borough of Tower Hamlets, Warwick District Council and Wigan Council all face the ICO’s scrutiny until November 30, with the monitoring period having started on September 1.
Each council was the subject of "a significant number" of complaints to the ICO over their response time to Freedom of Information (FoI) requests.
ICO deputy commissioner Graham Smith said: "The four councils we have named today should see their inclusion on the latest monitoring list as a clear signal that they need to improve their practices.
"Responding to FoI requests within the permitted timeframe is one of the cornerstones of ensuring transparent local governance. We will be happy to work with the councils in their efforts to turn their performances around."
All public bodies are subject to FoI requests for public information, and have a duty to respond within 20 working days.
The ICO said it remains concerned over the Metropolitan Police’s own response times, which is still failing to respond to 85% of requests in time despite "numerous" internal changes, according to the body.
CBR waited two months for a response to an FoI request enquiring how many Met computers were still running the Windows XP operating system after Microsoft had ended support for it.
The ICO will meet with senior Met representatives in the coming weeks to decide whether further action is required.
It praised the BBC and Essex Police after it monitored the two organisations between May 1 and July 31 over their FoI response times.
Smith said: "We are pleased that the BBC and Essex Police have risen to the challenge after being placed on our FOI monitoring list. The monitoring exercise should be seen as a wake-up call to authorities to address the problems they are having.
"Both of these organisations should be proud of the changes they have made to make sure requests are responded to in a timely fashion and we expect these improvements to continue."
The ICO is still considering the performance of Greenwich Council, also monitored over that period, while it reported improvements in the Cabinet Office and Crown Prosecution Service’s response times following monitoring, both dealing with more than 90% of FoI requests within the 20-day deadline.