Merton Council is proposing a rent-free deal to the Metropolitan Police Service (MPS) if they agree to return police officers to a former police base.
The police office in Pincott Road, South Wimbledon closed in September last year in a £500m round of cuts to the police force.
Safer neighbour team (SNT) officers who served Colliers Wood and Abbey wards from the base were relocated to Mitcham or Wimbledon police stations.
Following complaints from residents about a rise in burglaries and anti-social behaviour around the High Path estate, councillors and residents are calling for police to return to their streets.
Nigel Skayman, chair of the Abbey ward safer neighbourhood panel, said: "The issue is we are not seeing neighbourhood policing. It's desperate. Police don't know what peoples' problems are if they are not here.
"The Met is prioritising one area in the borough, not the whole borough."
Highlighting the breakdown of relations between police and the public across London, Mr Skayman said: "They need to start building bridges and building bridges quickly."
Police executed seven warrants targeting anti-social behaviour on the High Path estate on February 22, with one person arrested for possession of class B drugs.
Councillor Andrew Judge, member for Abbey ward and cabinet member for environment and regeneration, has written to Superintendent David Palmer asking him to consider returning officers to the base.
Coun Judge said: "Residents are concerned about groups of youths acting in an intimidatory manner, enagaged in drug dealing and graffiti.
"In the past a number of parts of the High Path estate were prone to these issues and regrettably that is becoming so again. Only recently in the tower blocks, have noted a resurgence of these concerns as well as visual graffiti in the stairwells."
Metropolitan Police have not responded to requests for comment.