The restaurant, which will take inspiration from the Loire region of France, will be on the site of the Green Man & French Horn pub on St Martin's Lane in London, just around the corner from the pair's first restaurant, Terroirs.
Building work is currently being carried out on the former London pub to develop it into the new restaurant with the majority of the work aiming to be completed before the start of the London Olympics.
Barker said: "It's an empty shell at the moment and we're just deciding where everything should go. We have no idea how the Olympics are going to affect our access, like how builders can get things like skips to and from the site, so we need to get things done before they start and be at the finishing stage from then."
The restaurant's style is expected to be 'fresh and simple' rather than 'a restaurant filled with bistro furniture' said Barker, who also said there were no plans to change its name.
"All the names of the restaurants we have thought about, but no-one could spell them or find them so we thought let's just leave this one as it is," he said.
Wilson is expected to be in charge of the Green Man & French Horn's kitchen initially. Menus will be inspired by food from the Loire with ingredients from the region likely to be used in dishes rather than traditional dishes from the region featuring on it.
The wine list will be exclusively from the Loire with more unusual wines from the region due to be highlighted.
"A lot of the wine that we enjoy drinking comes from the Loire," said Barker, "so it seemed like a good idea to focus on them. We wanted to also highlight some of the more unusual wines rather than the ones everyone knows. We're going to visit the region and source some new vintages."
Barker, who opened his third venue, Soif on Battersea Rise last November with Wilson, said the latest restaurant was part of he and his business partner's plans to open individual restaurants rather than rolling out one concept.