BT will close its dial-up internet service on September 1.
The move has raised fears that customers in rural areas could be left without a web connection.
But the telecoms giant has assured clients they will not lose out and can either switch to broadband or an alternative service.
These options are cheaper than the old dial-up - or narrowband - service, BT said.
The company contacted several thousand customers in June to warn of the changes.
Those who cannot get broadband - an estimated 1,000 homes - were offered another narrowband service.
A spokesman said: "BT can confirm it is closing its dial-up service in September.
"This is a legacy product that is only used by a tiny number of customers, most of whom can easily transfer on to broadband for a cheaper price.
"Our estimate is that only 1,000 of the current customers will be unable to access broadband following the change but they will continue to have dial-up access via PlusNet should they choose to, once again for a cheaper price.
"No one is being left without the option of an alternative service."
According to BT, PlusNet's narrowband service is £2.26 per month cheaper than its own offering.