"Eight people have been arrested on suspicion of interfering with public infrastructure", said a police statement, adding that "heightened police presence should be expected".
Gatwick, Britain's second-busiest airport, was operating normally according to an airport spokesman.
Just Stop Oil said seven protesters were involved in the disruption, with a video on the group's social media showing activists sitting on the floor blocking an entrance to the departure gates.
Passengers appeared to step over the protesters to get past them.
Last week, several pressure groups demanding governments sign an international treaty phasing out oil, coal and gas extraction and use by the end of the decade staged protests at airports across Europe.
Ten JSO supporters were arrested for planning to disrupt London Heathrow airport, with protests also taking place in Germany, Norway, Finland, Spain, Switzerland and Austria.
Heathrow and Gatwick airports sought court orders to stop environmental activists from entering their property.
The summer travel season protests are organised by climate groups from 10 countries part of the "Oil Kills" coalition.
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