The network's UK chief executive, David Dyson, has previously said he believes 5G has the potential to end the need for fixed broadband.
However, in a trial offered to BBC News prior to the public launch, the signal was found to be flaky.
Three said it was investigating why problems had been experienced.
A spokeswoman told BBC News the company had received positive feedback from others who had taken part in its beta tests.
"We appreciate the feedback on the initial testing pre-launch and as part of our ongoing commitment to ensure all customers receive a great 5G home broadband experience, we will be constantly optimising and enhancing the service to ensure customers benefit from our expanding 5G rollout," she said.
CCS Insight analyst Ben Wood said the launch marked a "tentative step" into the 5G market for Three in the UK.
"Three UK is in pole position when it comes to its potential with 5G, given the huge slice of spectrum it owns," he said.
"The 100MHz of contiguous spectrum is the optimal package when it comes to rolling out 5G technology.
"This is a first toe in the water for the 5G service and I guess we will really find out what Three can offer when the wider 5G network is turned on and you can use it with a smartphone."