Carphone Warehouse said it had been overwhelmed with calls for its "free" broadband service Talk Talk and had signed up 340,000 customers --almost double the number it anticipated when the service launched in April.
But it admitted customers were having to wait up to three months to go live, with those signing on today not being connected until August.
Carphone, Europe's largest mobile phone retailer, said it had connected more customers to the service in the first eight weeks than it had planned to do in the first four months.
Chief executive Charles Dunstone has written in a blog on the Carphone Warehouse website about his "immense frustration" over the company's difficulty in coping with the 20,000 calls it has been taking every day from people inquiring about the service.
Mr Dunstone remained upbeat yesterday and said he was committed to making Talk Talk "more of a household name than it is and the number one alternative residential telephone company to BT".
He thanked customers for their patience and understanding as the firm "strained to cope with the calls and emails".
Reporting a 36 per cent increase in pretax profits to £136.1 million and 29 per cent growth in revenues to £3 billion for the year to April 1, Mr Dunstone said: "Our aim was to change the UK broadband market forever, and there is no doubt that we are well on our way to achieving this."
The company and City analysts had anticipated around 170,000 new customers would sign up.
Carphone believes people are prepared to wait for a service that is free. All customers are given a go-live date when they sign on, which is generally two to three months later, but all are getting connected before the anticipated date, a spokesman said.
Keith Bowman, equity analyst at Hargreaves Lansdown Stockbrokers, said: "While a great deal of comment and concern is being expressed with regard to the delay in connecting these new customers, a confident management will see this as a 'great problem to have'." He added: "The market consensus opinion is likely to remain resolutely positive."
When Carphone launched the offer - which costs £21 a month through subscription to Talk Talk, bundling broadband with UK and international calls to 28 countries - only 150,000 of its 2.6 million customers used broadband.
Around 60 per cent of the new customers are first-time broadband users, the spokesman said, adding it would soon be as common as televisions in people's homes.
Until now, Carphone has been hampered by having to resell BT's wholesale broadband product. But it is investing £60 million to install its own broadband equipment in 1,000 BT exchanges - a process known as loop unbundling.
Carphone said it was on track to start the migration to unbundled lines in July.
This will allow it to reach 70 per cent of the population.
It intends to continue the expansion of its store portfolio and has a target of 15 per cent growth in mobile connections over the coming year, Mr Dunstone said.
Carphone's broadband initiative has triggered a raft of competing deals.
Last week, mobile phone giant Orange launched its "free broadband" offer available to customers signing up for a mobile phone contract worth at least £30 a month. Satellite broadcaster BSkyB is widely expected to unveil its own broadband deal in the coming weeks.
"There will be more competition. We haven't seen very much yet,"
Carphone Warehouse chief financial officer Roger Taylor admitted.
However, he was unfazed by the threat from Orange, saying mobiles and broadband were two different products.
"Not every buyer of a mobile phone is going to be the decision maker when it comes to broadband," he said.