However, a small number of people in rural areas where broadband will not work will struggle to get online after the change.
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 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, the BBC quoted the company as saying.
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. The distance means that the broadband signal degrades," he said.
Those who had to stick with dial-up would still be able to get such services from BT via its Plusnet subsidiary.
"No-one is being left without the option of an alternative service," said a BT spokesman.
Dial-up service involves modems sending data over lines more typically used for voice calls.
The best dial-up modems sent data along telephone lines at speeds of up to 56 kilobits per second, although compression could be used to improve this top speed.
By contrast most broadband technologies work in the megabits-per-second range.
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.
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