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Travellers have set up camp at Luton Recreation Ground - a beauty spot frequented by children and dog-walkers.
Five caravans arrived at the council-run park in Capstone Road, Chatham, this morning.
It is thought they got in through the Ash Tree Lane entrance.
They set up awnings and deckchairs to make the most of the heatwave.
One vehicle has deckchairs outside it and has its awning down.
Medway Council is aware the group has arrived on the site.
A spokesman said: “We have visited the site and will be following a civil legal process to move the group on.”