Its figures provide the first firm evidence of the extent of web paedophilia, which BT is targeting with its Clean Feed system.
The Internet Watch Foundation called the figures “staggering” and said children were being abused in order to supply the hardcore images.
Police officials said the extent of the online porn problem was “extremely disturbing”.
BT said in its first three weeks its new system, which bars access to particular sites, registered nearly 250,000 attempts to view web pages containing images of child pornography.
That represents an average of about 10,000 requests each day.
Pierre Danon, chief executive of BT retail, said the company was blocking access to hundreds of sites which had been identified by the Internet Watch Foundation.
But he said BT did not track those trying to log onto the sites or pass their details on to police.
And he said the company had no way of telling how many users were navigating to such sites by accident.
“We don’t know their motives or who does it and honestly we don't want to know,” he told BBC Radio 4’s Today programme.
A BT spokesman added: “It could be that one dedicated pervert is making hundreds of attempts to get on websites each day.”
Currently the technology is only blocking BT Retail’s 2.5 million internet customers from viewing child porn sites but Mr Danon said the company would make it available to other internet service providers on a non-commercial basis.
British Home Office minister Paul Goggins said the figures revealed by BT were “deeply shocking” and he said he hoped other service providers would take up the offer of using BT’s blocking technology.
He told the Today programme: “Every image of a child that appears on the internet is an image of a child that’s abused.”