BT will turn off its dial-up internet access service on September 1st 2013.
The telecoms firm said it was taking the step because such a small portion of its customer base connect using dial-up connection.
It added that the vast majority of its 6.8 million broadband customers had switched to much faster connections.
But following the deactivation, a number of users in rural areas will struggle to get online as broadband is not available where they live.
Dial-up customers were first informed about the impending closure in May and June this year, BT said, adding that most of these people would be able to migrate to a broadband service.
The company said that the shut-down meant about 1,000 people who lived in remote areas would not be able to move to broadband as their phone line was incapable of supporting the technology.
These people were likely to be living in some of the most remote parts of the UK, said Oliver Johnson, chief executive of broadband consultancy Point Topic.
"They will be too far from the telephone exchange to get any meaningful broadband," he said. "The distance means that the broadband signal degrades."
"No-one is being left without the option of an alternative service," said a BT spokesman.
Sebastian Lahtinen from the Think Broadband news site, said the closure was a sign of the times.
"It's a statement of how mainstream broadband services have become, with entry-level broadband being cheaper than the dial-up plans BT is closing down," he said.
About 800,000 people still used dial-up in 2010, the last year for which figures were available, said an Ofcom spokesman.
"The number has now fallen so low nationally that it's quite difficult to get any accurate figures from a survey sample," he said. "We think it's in the very low hundreds of thousands but we cannot be any more confident than that."
With the vast majority of exchanges equipped to use broadband technologies such as DSL there was little reason to stick to dial-up, he said.