Reports of the first few caravans occupying the land surrounding the Telephone Exchange building on Gorgie Road came in May, but the number has since grown to around 15 of them parked in the car park area.
Residents of Coxfield have claimed that those living in the caravans are causing environmental and health risks to those living in the surrounding area by using the car park that they are occupying as a toilet.
A BT spokesperson said: “We became aware of travellers on BT land at Gorgie Road on Friday.
“As we have an operational site on this land, extra security was deployed.
“An eviction order was granted yesterday and we expect the site to be vacated later this week.”
The residents have also made claims that the travellers are littering over the fences of residents, generating noise until the early hours of the morning, and smoking outside residents' windows.
A Police Scotland spokesperson said: “Police in Edinburgh are aware of a traveller encampment, which has been set up in the Coxfield area.
“Officers have been engaging on a daily basis with those within the encampment and we continue to monitor the situation alongside our colleagues within the City of Edinburgh Council and the landowner.”
Additionally, another caravan encampment has also been growing in numbers in Kings Place, Portobello.
Residents in the Portobello area who have been in touch with their local councillors have mentioned their concerns for their own safety.
Speaking about the caravans at Portobello, a council spokesperson said: “We have been working very closely with the Police, elected members and the local community to look at options which will restrict long-stay parking along Kings Place.
“Currently, there are no parking restrictions in this area which means any vehicle can park as long as it is not causing an obstruction, but we are consulting with residents to see how this might be improved.
“We are aware that a number of caravans are parked along Kings Place and our housing officers have visited the area.
“Our environmental wardens, along with Police Scotland have also been involved in a joint initiative to patrol the area.
“We have found no evidence of anti-social behaviour or obstruction associated with the caravans to date, but we take residents’ concerns and those of local businesses very seriously and will investigate any reports.”