Announcing the news via The Fix's Instagram page yesterday (6 July), Kenny said: "Sad news unfortunately. We won’t be returning.
"Covid-19 has hit our industry hard and made it to difficult for us to now run this concept in this space.
"The hotel, however, will continue to offer a drinks offering in the building.
"A huge thank you to everyone who’s joined us over the years and enjoyed a drink here. Big thanks to all the bartenders who tirelessly improved the bar with their hard work."
In a separate post, also published yesterday, The Set did confirm it would be reopening at some point, but that the date was yet to be confirmed.
It said: "Due to the impact of Covid-19, we’re having to make some changes here at the restaurant.
"We don’t quite have a starting date yet as we’re holding tight and seeing what happens over the next few weeks. It’s crucial we time this well for several reasons.
"When we do return, we plan to operate four to five nights a week on one extended tasting menu. The plan is to create a really special dining experience. Multiple courses, drinks pairings and hopefully a really memorable meal for you. Similar to our “chefs table” experience, but bigger, better and more thoughtful.
"Thus meaning we’ll no longer be running breakfast, lunch or Sunday service. We’re are very proud of the offerings we had in place for these time’s and like to think we’re ending them on a high note.
"Big thanks to everyone who has supported us and continues to do so."
Kenny launched The Set in 2015.
In 2017 he also took over responsibility for the Artist Residence's breakfast offering, and then in 2018 was put in charge of the hotel's entire F&B operation.