The Landscape Group currently delivers grounds maintenance under a 10 year contract begun in 2008, and under new plans the contract would be extended until the end of March 2019. The council is planning to merge the community engagement and development functions with operational delivery.
Unite regional officer Onay Kasab said the union was concerned that the privatisation of services would cause a "race to the bottom" in terms of pay and conditions.
"Companies are designed to make a profit and they just need a business reason and they can start reducing wages or numbers of staff," he said.
Unite is also seeking legal advice over the process of privatisation, Kasab said. He said there could be a legal issue with the takeover of the Landscape Group by French company idverde, which "wasn’t reflected in the decision", he added.
A spokesperson from Bromley Council said that council regretted that further industrial action is being considered and said it "will only consider outsourcing if it represents good value for residents" and options including continuing to provide services in-house or facilitating social enterprise are also considered.
"The Council has to identify £50 million savings over the next four years from a net budget of around £200 million so it is inevitable that some services will have to be provided in different ways into the future."
The spokesperson added: "The Council is varying its existing grounds maintenance contract and by merging the community engagement and development functions with operational delivery, we will deliver a more locally focussed operation which both protects the service and delivers much needed savings."