Travellers who moved onto an open space in Medway have claimed to council officials they have Covid-19.
Caravans started appearing on the land in Chestnut Avenue, Walderslade, on Friday night, with more joining yesterday.
There are around 10 mobile homes there.
Cllr Adrian Gulvin (Con), who represents Walderslade, explained Medway Council and police had visited the encampment to complete welfare checks.
He added: "Officials were told a couple of them have Covid. The ward councillors have been in contact with the Director of Public Health to arrange for testing and inoculations for them.
"Until it is proven they haven't got the virus we cannot move them on, where it could be spread throughout different locations. That would be totally irresponsible.
"The first stage of the legal process on eviction is the welfare checks, but everything has to go on hold until we can determine the Covid status. That's why urgent work is happening with the public health department."
But one resident claims to have seen some people at the site continue to come and go and raised fears that this could still potentially spread any Covid-19.
The resident, who asked not to be named, added: "I haven't seen much evidence of social isolation. It surely must be easy to get lateral flow tests delivered as soon as possible as we're worried about the risks to health of people nearby."
He added: "We've experienced noise with people arguing among themselves and local dog walkers who use the field for recreational purposes.
"Their dog is attacking local dogs and the field is no longer available to use without feeling intimidated. We are concerned more will join them, making even more noise and mess."
Medway Council has been approached for comment.