Parking attendants have called off a 24-hour strike planned for Saturday after their employers said they would reconsider new rules about breaks.
Vinci Park provides all street parking attendants for Bromley
Traffic wardens feared Vinci Park's plan to make them take breaks in public places increased the risk of abuse as they could see people they had fined.
Formerly the wardens, who patrol Bromley, south-east London, went to the civic centre's staff canteen.
Vinci Park said it will look into other venues for staff breaks on Monday.
The RMT says it is open to suggestions for alternative arrangements but the emphasis was on safety.
Sixteen of the 19 RMT members balloted over a possible strike voted in favour of industrial action, while three did not return a vote, the union said.
RMT general secretary Bob Crow said: "Parking attendants run a daily gauntlet of abuse and threats, and physical assaults are a regular occurrence, yet the company imposed changes that expose our members to an increased risk of attack.
"This is a very straightforward dispute. The company needs to understand that it cannot continue to put its profits ahead of employees' safety."
Vinci Park provides all street parking attendants for the London Borough of Bromley.