LONDON — Officially, it is 20 Fenchurch Street. To Londoners, it is the “Walkie Talkie,” so named for its unique shape, with the building bulging out as it rises into the British capital’s skyline.

On Thursday, the 37-story office block was sold to LKK Health Products Group, a Hong Kong-based company best known for making Lee Kum Kee oyster sauce, for 1.3 billion pounds, or about $1.7 billion.

The Walkie Talkie has not always been so highly coveted.

The building was criticized almost immediately after it opened in 2014. Rowan Moore, an architecture critic for The Observer newspaper, described it as “bloated, not elegant.”

“It has no meaningful or enjoyable relationship to anything else, either at street level or on the skyline,” Mr. Moore wrote at the time.