In a recent Instagram post, Cenci said the decision to permanently close the site came as a direct result of the Coronavirus pandemic.
He said: "It's with a broken heart and a decision that I thought I would never have to take, but we have decided not to reopen Loyal Tavern.
"As a direct result of the Covid-19 pandemic combined with fixed costs, we simply can not continue to operate.
"It has been an extremely challenging time for everyone in our industry, and I can only hope things will get better."
Cenci, who was previously executive chef at Duck & Waffle, opened Loyal Tavern in partnership with White in September 2018, taking over the former Village East site.
The concept was designed to showcase ‘inventive small plates, brought about by a love of local sustainable ingredients’, and the menu featured dishes such as Cornish mackerel with apple, pine nut and truffle; and venison tartar with beef dripping.
In his statement, Cenci added: "I'm not sure what the future will hold for me now, but I'd like to say a huge thank you to all the team at Loyal Tavern whom all of which I would happily recommend for work and to all the guests who had the chance to dine with us.
"Thank you for your support."
Cenci cooked at London’s Noble Rot and Michelin-starred Restaurant Laurent in Paris before joining Duck & Waffle as senior sous chef ahead of the sky-high restaurant’s opening in 2012.
He worked alongside then-executive chef Dan Doherty to develop the menu, which included ox cheek doughnuts and foie gras crème brulee.
During his tenure Duck & Waffle ranked 29th in Restaurant magazine’s National Restaurant Awards top 100 list in 2016.