The report comes as concerns grow about the ability of infrastructure companies, such as BT, to manage natural monopolies, Demos said.
Putting control of the local loop in the hands of a public interest company would maximise the number of service providers that can use the shared infrastructure and increase innovation with networks, said James Wilsdon, head of strategy at Demos and co-author of the report.
"While there may be short-term advantage in allowing BT to roll out broadband as quickly as possible, there are longer term risks," he said. "The UK is sleepwalking towards a broadband monopoly, with little opportunity or incentive for innovation within the network."
Ofcom should conduct a cost-benefit analysis of breaking up BT soon, the Demos report concluded.