Carphone, founded by Charles Dunstone, its chief executive, is understood to be among a group of mobile phone and broadband internet players to have sought information on the AOL sale.

Mr Dunstone, whose business is on the brink of entering the FTSE 100 index for the first time, said that he would keep “a close eye” on the sale of the AOL business, which Time Warner, its parent, has put on the market amid concerns over fierce competition.

However, he said that he felt “no pressure” to make acquisitions while Carphone continued to grow organically at such high rates. Shares in the company rose 8.5p to 340p yesterday, after Carphone said that it had signed up 340,000 new customers to the “free” broadband package that it launched in April and reported a 36 per cent rise in full-year profits to £136.1 million on revenues up 29 per cent to £3 billion.

AOL, which has 2.2 million customers, is a valuable asset because of the market share that it offers. It is the UK’s third-biggest internet service provider behind BT and the combined NTL/Telewest cable group. Other potential buyers include Vodafone and O2, the mobile groups. Both want to move into broadband. BT and NTL are also regarded as potential bidders, but could face regulatory problems.

Some industry players said that the £1 billion price tag on the business looked “aggressive”, given the falling price of internet access and the imminent entry of strong new competitors, such as BSkyB and NTL/Virgin Mobile.

Analysts said yesterday that they were surprised by how rapidly Carphone Warehouse’s broadband offering had been taken up. The City had predicted that it would have attracted up to 100,000 customers by this stage. Carphone declined to reveal details of its customers, but said that 60 per cent were new to broadband.

Analysts are concerned about the group’s ability to cope with so many new customers. Richard Ireland, head of telecoms for Ernst & Young, said: “The challenge is in the execution and the ability to meet service expectations. You only have to cast your mind back to Bulldog (Cable & Wireless’s broadband business), which was in a similar position, to realise that getting this number of customers up and running is not a trivial exercise.”

Mr Dunstone conceded that the group had struggled to cope with demand but said that he was dealing with the problem by recruiting new customer service staff.

Although Carphone benefited as a “first mover” by offering its free broadband early, competition is set to get fiercer. BSkyB, in which The News Corporation, parent company of The Times, has a 37.2 per cent stake, is about to launch its own service while Orange last week launched its “free” service.

Mr Dunstone has ruled out any move to combine mobile phones with his broadband package.

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