A fresh corporate comms strategy has now been drafted and will be presented to the cabinet in September.
This will tell councillors that the affect of negative publicity of the council's role in the eight-year-old's murder cannot be ignored.
An increase in public affairs and media relations at a national level is being recommended as a priority, with a series of visits for 'opinion-formers', such as journalists, Transport for London officials and London MPs, being organised.
Comms head Julie Hollings said: 'We need to focus attention on what is being done to improve and the good work that is going on across the council.
'This isn't about blowing our trumpet - the key is about being open,' she added.
At the inquiry into the Climbie case, care workers were accused of not doing enough to prevent her death and the council was accused of incompetence and covering up evidence after documents about the case were mislaid.
And last month a damning report by the social services inspectorate found that many family support workers were too inexperienced due to a high staff turnover.
The report also highlighted a 'blame culture' with frontline staff complaining of a lack of support from senior managers. Poor communication with stakeholders and service users was also highlighted.
Changes have already taken place including a £3.5m rescue package to help recruit and retain children's social workers and offer pay rises.
Also, Marina Pirotta Communications has been hired to review how the social services department's publications, brand image and online activity can be improved. MPC director James Flynn is leading the account team, which will conduct interviews with service users and local stakeholders such as teachers and GPs.