An inquiry report by the borough's child protection committee found care of the child Mia Gibelli was blighted by 'a series of omissions, oversights, procrastinations and failures to communicate'.
A case conference to discuss the family was not scheduled until the day Mia died - a date which may in itself have added to the pressure on her mother Christine Gibelli, the Guardian says.
Mrs Gibelli had attempted infanticide in the past and two of her other children had been placed on Lambeth's at risk register.
Lambeth Leader Steve Whaley said: 'The council accepts the errors made in this case. However, there is no denying the workload placed upon staff poses great difficulties in their struggle to act in the best interests of the many children in need'.
Junior health minister Tim Yeo said: 'It does defy belief that there should have been such a poor level of communication, such a wholly inadequate response, given the nature of the nature of the tragedy which was all too likely to occur under these circumstances'.
Mrs Gibelli appeared briefly at the Old Bailey yesterday when a judge ordered her to remain in a hospital secure unit.