O2, Three, Vodafone and EE each said their customers had been affected by the problem, which is said to have originated in equipment that connects the different mobile networks together.
The companies said a joint meeting will now be held to discuss the issue to ensure it does not happen again.
The fault came as millions of people began working from home as part of Government guidance to reduce social contact to help stop the spread of coronavirus.
In a statement, a spokesman for EE said: "A technical incident with equipment that connects the UK's mobile networks together has caused some customers to have problems making phone calls today.
"Data was not affected, and emergency 999 calls were completed successfully. This was not related to any increase in calls created by a rise in working from home."
O2 said the networks were all now working together to ensure such an incident does not occur again.
"Today the industry experienced an issue that meant some calls between different networks were unable to connect," the company said.
"Specifically, O2, Vodafone and Three were unable to connect to EE, and EE customers were unable to connect to O2, Vodafone and Three.
"At a time when the country needs connectivity most, it is important we work together rather than pointing fingers before facts have been determined.
"As this was a problem for multiple networks, there is a National Emergency Alert for Telecommunications and Ofcom call this afternoon to determine the route of the issue to ensure this doesn't happen again."
The issue was first reported on Tuesday morning when O2 said it was aware of a problem with its "voice services" and apologised to customers.
Three UK then also confirmed an issue with voice calls was affecting "around 3%" of customers, while Vodafone said around 9% of calls made over 3G had been affected.
The outage was quickly spotted by users, with many going to network status monitoring website Down Detector, as well as social media, to report issues across all four major networks.