Around 750 Building Safety Regulator (BSR) registration applications have been started since the process opened last month.
The BSR is pleased with the early response from the building industry but is urging all owners and managers to act now.
Up to 12,500 buildings in England (high-rises at least 18m or have seven or more floors containing at least two residential units) are covered by the new regulator which all must now be registered with it by law.
Those responsible for the safety of buildings have until the end of September to register or face prosecution.
Building owners or managers must provide the number of floors at or above ground level, height, amount of residential units, and year of construction.
Philip White, HSE’s director of building safety, said: “Registration is a crucial part of the new regime and our efforts to ensure residents of high-rise buildings feel protected and safe in their homes.”