Universal high speed broadband is to be delivered by a regulatory Universal Service Obligation (USO), the government has confirmed.
The decision means that everyone in Britain will have the legal right to request minimum speeds of 10Mbps by 2020.
According to the government, this is the speed that will meet the typical needs of a family that wants to browse the web, stream films and carry out video conferencing at the same time.
BT had volunteered to deliver universal high-speed broadband to all areas of the UK, as an alternative to regulation.
However, the government has decided that this plan was not "strong enough for us to take the regulatory USO off the table".
Karen Bradley, the Culture Secretary, commented: "We are grateful to BT for their proposal, but have decided that only a regulatory approach will make high speed broadband a reality for everyone in the UK, regardless of where they live or work."
She went on to stress that broadband is very important to homes and businesses and said everyone should benefit from a fast and reliable connection.
"This is all part of our work on ensuring that Britain’s telecoms infrastructure is fit for the future and will continue to deliver the connectivity that consumers need in the digital age," Ms Bradley added.
The government believes the regulatory approach offers a number of benefits to consumers, such as the fact the minimum speed of connection can increase over time as people's connectivity requirements evolve.
Furthermore, it said the USO provides for greater enforcement to help make sure homes and businesses get connected, as well as maximise the provision of fixed line connections in the hardest to reach areas.
BT has said it "respected" the government's decision, before adding it wants to "get on with the job of making decent broadband available to everyone in the UK".
"We'll continue to explore the commercial options for bringing faster speeds to those parts of the country which are hardest to reach," a spokesperson said.