The opening marks the next stage in the development of the Bun House brand, which in February established a new flagship site in Chinatown.
According to the Box Park website, the Wembley menu features new additions such as a beef brisket bun; and a brioche-style pineapple bun.
The menu will also include favourites from the Chinatown site including the pig bun with char sui pork belly; a cumin-spiced lamb bun; and a sweet custard bun.
Peffly and He opened the original 10-cover Bun House on Greek Street in Soho in early 2017, with a focus on Chinese-style bao that, unlike the Taiwanese buns popularised by the likes of Bao and Flesh & Buns, are served closed with the filling inside.
However, the size of the Soho site meant it had a limited production capacity, leading the pair to move the operation to a larger location on Lisle Street in Chinatown.
They then converted the Greek Street site into Wun's Tea Room & Bar; a Hong Kong-style concept partly inspired by He’s upbringing, which opened in July.
Speaking to BigHospitality in August, Peffly and He said they believe the Bun House concept offers great opportunity for expansion, with plans to open more satellite Bun House locations within food halls and markets in the near future.