When the scheme is complete in 2008, subscribers should be able to access the internet from laptops while sitting in the park, the library or the pub.
WiMax, the next generation internet technology, offers a more powerful signal than that offered by Wi-fi, and is increasingly available in cafés. Its transmitters can send signals directly to computers from as far as five kilometres away, compared with 50 metres for Wi-fi.
Pipex has formed a separate company, Pipex Wireless, to roll out the new network.
It should be available to residents in Manchester and London in 2007 and to eight more big cities by 2008. Eventually, up to 50 cities across the UK could have the new networks.
Pipex holds one of only two WiMax licences that are available in the UK. The other is held by Hong Kong's PCCW.
Last week, the telecoms watchdog Ofcom relaxed the competition rules, which allowed Pipex to offer WiMax commercially.
The new initiative raises the question of whether BT's plan to install Wi-fi across Britain will be profitable. BT is aiming to provide blanket Wi-fi in the UK, starting with 10 cities this year. The telecoms giant hinted yesterday that Pipex may be getting ahead of itself.
A BT spokesman said: "BT is actively involved in the development of WiMax and expects to be a major player when the technology has developed further."
BT insiders have poured cold water on suggestions that it wants to buy Pipex. Some analysts believe that WiMax will eventually supersede Wi-fi, although the two technologies are compatible.
Intel, the world's biggest maker of computer chips, is investing £14m in the new company in exchange for a stake of less than 50 per cent. It will also provide technical support. A further round of funding is likely in the near future.
Peter Dubens, the Pipex chairman, will head the new company, although a management team is being hired. He conceded that telecoms companies are always at risk of being overtaken by new technology but said he is optimistic about this deal. "If WiMax does what it says on the tin, this is a very valuable company," Mr Dubens said.
Pipex made a profit of £7.1m in 2005, it said yesterday, up from £6.2m for the year before. Sales increased 30 per cent to £102m. The shares closed down 0.5p at 15p yesterday, giving the company a value of £347m.
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