The contact tracing app, available on smartphones, was downloaded by 6 million people in England and Wales on its launch day last Thursday, the government said.
Health secretary Matt Hancock said the response had been “absolutely fantastic” so far.
The app’s rollout had been criticised by some users who were unable to download it as their Apple iPhones are too old to run the iOS 13.5 version of the device’s software.
On Friday, it suffered a glitch that meant it was unable to link more than 60,000 coronavirus tests carried out that day to its systems.
From Monday, it is illegal in England to not enter self-isolation if told to do so by a staff member of NHS Test and Trace, with fines of up to £10,000.
However, Hancock said it will not be illegal to ignore the app if it tells you to self-isolate.
Read more: The NHS COVID-19 app – how it works and other key questions