BT says it is blocking up to 20,000 attempts each day to access child porn.
The scale of child porn use on the net has alarmed watchdogs
Its figures provide the first firm evidence of the extent of web paedophilia and BT is targeting the porn 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.
Anyone trying to access such a site would be presented with a message reading "Website not found".
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.
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."
The BBC's Neil Bennett said even allowing for some people making repeated attempts, it is clear thousands of people are trying to see such material daily.
BT is only one of the main service providers in the UK and police leaders are calling on others to block paedophile websites.
Websites assessed by the IWF as "illegal to view" under the 1978 Child Protection Act were targeted by BT.
The IWF keeps a real-time live database which is updated every time an illegal site is found. At any one time there are thousands of sites on the database.