All UK homes and businesses will have access to "fast broadband" by 2020, David Cameron has pledged.
The PM is to introduce a "universal service obligation" for broadband, giving the public a legal right to request an "affordable" connection.
It would put broadband on a similar footing to other basic services such as water and electricity.
Labour said it meant "another five years on the broadband back-burner" for those struggling with their service.
In 2010, the coalition government promised the UK would have the best superfast broadband in Europe by 2015.
Then, in 2012, a pledge was made by then-Culture Secretary Jeremy Hunt that the UK would have "the fastest broadband of any major European country" by 2015.
He defined high-speed broadband as offering a download speed of greater than 24 megabits per second (Mbps). Communications regulator Ofcom defines it as 30Mbps.
Mr Cameron's latest announcement is aimed at ensuring consumers have access to a broadband connection with a speed of at least 10Mbps, no matter where in the country they live or work.
"Access to the internet shouldn't be a luxury, it should be a right - absolutely fundamental to life in 21st Century Britain," he said.
Mr Cameron, who is expected to set out further details next week, added: "Just as our forebears effectively brought gas, electricity and water to all, we're going to bring fast broadband to every home and business that wants it.
"We're getting Britain - all of Britain - online, and on the way to becoming the most prosperous economy in the whole of Europe."
Officials said that more than 83% of homes and businesses in Britain currently have access to a superfast broadband connection - 24Mbps - with that number set to rise to 95% by 2017.
Culture Minister Ed Vaizey told BBC Radio 4's Today programme: "We want to upgrade the universal service obligation to provide fast broadband speeds of 10Mbps for the very hardest to reach homes and businesses. Those at the end of the line, the last 5% that we are desperate to get to.
"So we're putting in place this regulation, that we're going to consult on at the beginning of next year, to make sure that if you're in that last 5%, you can demand, and you'll get it."
Chi Onwurah, shadow minister for culture and the digital economy, said the government needed to set out how the new pledge would be funded and when consumers would "actually see the benefits".
"Five years after abandoning Labour's fully-funded commitment to universal broadband, the government's "superfast" broadband rollout is still being hit with delays and at the mercy of a single provider," she said.
The government has already given BT £1bn to extend broadband to some rural areas, although its record has been criticised, BBC reporter Rob Young says.
It is unclear whether more taxpayers' money will be available for this latest ambition, he adds.
BT says faster universal broadband needs to be "commercially viable". Virgin Media has argued against state subsidies.
In a statement Tom Mockridge, Virgin Media chief executive said: "Government should roll back the red tape we already have today. Help us connect more premises more quickly by giving us the same fast-track access rights as water and gas companies."
In September, BT hit back at rivals calling for its break-up, as it announced a strategy to make the UK the fastest broadband nation.
It revealed plans to connect 10 million homes to ultrafast broadband (300-500Mbps) by the end of 2020 and raise the minimum broadband speed for homes that cannot get fibre to 5-10Mbps.