The unauthorised encampment was set up on April 8 at Eling car park near the cemetery.
Council officers from New Forest District Council (NFDC) and police officers attended the site last week.
Nearly a week since their arrival, the group has left the area, and Cllr David Harrison is asking for preventative measures.
In a post on Facebook, the Liberal Democrat for Totton South said: “Thanks to the officers at NFDC and the police, the travelling encampment which settled for a time at the Eling cemetery car park has now moved on.
“There is some litter clearance required. I understand that two people got bitten by free-roaming dogs belonging to the travellers. There was a bonfire on site. Two swans that were nesting on a nearby floating island have disappeared.
“I have asked Cllr Patrick Mballa to enquire whether we might avoid a further incursion by installing some sort of height barrier at the car park entrance.”
NFDC has been approached for a comment.