Dunstone, writing in his blog on the Talktalk website, acknowledged that customers signing up now will have to wait until August to receive the free broadband offer.
Carphone Warehouse originally forecast 130,000 customers to sign up for the £20.99 a month Talktalk package, which includes free broadband, free UK calls and some free overseas calls.
The company will announce full figures to the City tomorrow, but it is reported the call centre is receiving more than 2,500 enquiries a day.
A Talktalk spokesman said: "The demand has been substantial, and a number of measures are in place to train people as quickly as possible. Everything is on schedule."
The spokesman would not say whether advertising would be scaled back because of the unexpected high demand. Agencies Clemmow Hornby Inge and HallMoore CHI worked on the campaign.
In a Daily Telegraph article, industry analysts Merrill Lynch today warned of technical problems with connecting high numbers of customers to broadband.
Rather than resell BT's broadband service, Carphone Warehouse wants to put its own equipment in BT exchanges as soon as possible, reducing what it pays to BT.
The mobile phone retailer is spending £110m on the switchover, know as "local loop unbundling", with a target of attracting 1.75m subscribers to broadband by March 2009.
In the Telegraph article, one analyst said: "Dunstone knows once people are with a broadband provider switching becomes a big hassle because they may be without a connection for weeks."
"Local loop unbundling is a slow and arduous process and the mighty BT can throw up any stumbling block it can think of."
Last week, Orange joined the broadband price war by offering free broadband to all new and existing subscribers spending over £30 a month. Vodafone is also believed be looking to purchase an ISP, with recent sepculation of a bid for Tiscali.
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