More than 10 million people downloaded the NHS Covid-19 app in its first three days, the Government has said, despite a raft of problems which saw users sent infection warnings that vanished without further information.

The Department of Health said that six million people downloaded the app on the first day, and there had been 1.5 million venue check-ins on Saturday.

But many users complained that they had received alarming messages from the app, saying they may have been exposed, even though they had not left the house since installing it.

Sean Eddleston, of Liverpool, said the notification disappeared as soon as he clicked on it.

“It was along the lines of I have been in close contact with someone who has tested positive, though I don’t believe there was any mention of getting a test or self-isolating,” he said.

“I was expecting more info once I opened the app, but nothing.”

The notification read: “Possible Covid-19 exposure. Verifying exposure info. The app has accessed the date, duration and signal strength of this exposure.”

Richard Coles, who lives in the North West, said he received a message at 1.04am. “Either it flagged someone walking past the house or it isn’t working properly,” he wrote on Twitter.

NHS Test and Trace initially said that the error was occurring if users had not selected England and Wales as their “active region”. But Mr Coles and others pointed out that the region was already set to England and Wales.

Katy McNally, also of Liverpool, wrote on social media: “This exact same thing has happened today to me. I don’t know what I’m supposed to be doing.”

Tristan Jakob-Hoff, a classical music writer and critic, said he had received a notification but complained there was no advice on the app. “Have I been exposed? How can I check?”

On Sunday afternoon, the Department of Health said that the notifications were default messages from Apple and Google, which could not be turned off.

“There is no need to be concerned if you miss or overlook them,” said an app-support help desk adviser. “Important messages from the app will always be visible to you from inside the app.”

The latest problems emerged just 24 hours after some users complained of not being able to upload test results, an issue that was fixed on Saturday evening. Oliver Dowden, the Culture Secretary, admitted there had been “teething problems” and insisted that the app was not a “core” weapon in the Government’s arsenal to tackle the virus.

But the Government said the app had received a “warm reception” overall from those downloading it, with an Apple store rating of 4.5 out of 5.

Matt Hancock, the Health Secretary, said: “The response has been fantastic. This is a strong start but we want even more people and businesses getting behind the app.

“The more of us who download it the more effective it will be.”

The Government said more than 460,000 businesses had embraced the app by printing QR code posters that link to it when scanned by customers.