The early demand for Carphone Warehouse's Free Broadband Forever product has nearly doubled expectations, according to the mobile phone retailer.
The company also said it is now aiming to bring forward by 18 months the installation of its broadband equipment in 1,000 BT exchanges.
The announcement, made on Tuesday morning, follows the news that new customers taking up the offer might have to wait months for the service to be provided, due to the unanticipated volume of subscription.
Chief executive Charles Dunstone told the City on Tuesday that take-up of the offer had "exceeded our most optimistic expectations". Around 340,000 customers are understood to have applied for the service in the two months since it was announced.
"When combined with our 2.6 million Talk Talk voice customers, our impact and influence on the UK residential telecoms market is becoming considerable," said Dunstone. "Our aim was to change the UK broadband market forever, and there is no doubt that we are well on the way to achieving this."
Analyst James Enck of Daiwa Securities agreed. "They're going from pretty much zero to being a top-tier player in a matter of weeks. I think it's a pretty impressive result," he told ZDNet UK.
"It works out to be about 6,200 [sign-ups] a day since the announcement was made," Enck continued. "Just over a third of those are completely new customers. If you assume that all the people who've signed up get provision, then Carphone Warehouse is in joint fifth place in the DSL market with Pipex at this point."
Enck also suggested that broadband was now "commoditised to the point where it's now a loss leader for something else", adding that Orange's announcement of a similar product last week was a validation of Carphone Warehouse's approach.
Carphone Warehouse began offering its broadband product to Talk Talk landline customers in April. For £9.99 a month and an additional £11 line rental, customers are offered free local and national calls within the UK, free landline calls to 28 foreign countries including Australia and the US, and up to 8Mbps broadband.