Other users reported that they were unable to make or receive calls after the alarm went off on Sunday
A review will be conducted to find out why a “very small proportion of mobile users” did not receive the test of a new national emergency alert system on Sunday.
The Cabinet Office said the “vast majority of compatible phones” received the alert as part of what was said to be the biggest public communications exercise carried out in the UK.
But the Government department said it was aware that the 10- second alarm and message notification was not delivered to some mobile phones.
Customers on the Three mobile phone network were among those to report not receiving the communication test.
The network provider said it would be working with the UK Government to understand what had happened.
A small number of people have also taken to social media to flag that they have not been able to make or receive calls since the 3pm alarm went off on their device.
The Cabinet Office stated that engineers had not spotted a trend of phone functions failing to work afterwards, but said officials were in the early stages of analysing the results of the trial run.
Once established, the emergency alert system is designed to warn the public if there is a danger to life nearby.
In future, a similarly loud notification and message will be sent to those the UK Government is seeking to reach.
The system is intended to be used in life-threatening situations including flooding and wildfires.
A UK Government spokesman said: “We have effectively completed the test of the UK-wide Emergency Alerts system, the biggest public communications exercise of its kind ever done.
“We are working with mobile network operators to review the outcome and any lessons learned.”
In a statement, a spokesman for Three said: “We are aware that a number of customers have not received the test alert.
“We are working closely with the Government to understand why and ensure it doesn’t happen when the system is in use.”
The loud alarm was planned to ring at 3pm on all devices that were using 4G and 5G networks in the UK.
For millions of phone users, the siren sounded for 10 seconds and displayed a message notifying phone users that no action was needed in response to the test.
Some smartphones also read out the message aloud to recipients.
On social media following the test, some users reported receiving the message a minute or so early, or even receiving repeat alerts.
Others said their phone received the notification after they switched it back on, having been off at 3pm.
Phones that were powered down or switched to airplane mode were not expected to sound.
Speaking before the test, Deputy Prime Minister Oliver Dowden conceded the drill could be “annoying”, but that it had the potential to save people’s lives once rolled out.
He told Sky News that the trial run was a “bit like when the fire alarm goes off at work”.
“It’s a bit irritating at the time but in the future people could be grateful for it because in a real emergency, this could be the sound that saves your life,” he told Sky News.
The Cabinet minister denied the new system was an example of nanny state interference, telling the BBC he did not accept “that characterisation”.
People who do not wish to receive future alerts will be able to opt out using their device settings but officials hope the life-saving potential of the messages means users will keep them on.
The test message that appeared on phones said: “This is a test of Emergency Alerts, a new UK Government service that will warn you if there’s a life-threatening emergency nearby.
“In a real emergency, follow the instructions in the alert to keep yourself and others safe.
“Visit gov.uk/alerts for more information.
“This is a test. You do not need to take any action.”
The Cabinet Office confirmed there was a spelling error in the Welsh language version of the alert text that was sent out.
For the translation of the English phrase “others safe”, the message reportedly read “eraill yn Vogel” when it should have said “eraill yn ddiogel”.
“A technical error caused one word in the Welsh language version of the emergency test alert to be misspelt,” a Government spokesman said.
“The fact that this occurred in a test alert will mean we can rectify it in future.”
The entertainment and sport sectors had been planning how to guard against disruption to large events when the test went off.
The London Marathon, Premier League football matches and matinee theatre performances were all taking place when the 3pm alert sounded.