Telewest is currently drawing up detailed plans for the service, which is due to be launched in the final quarter of the year.
However, one likely feature is that customers will pay only a flat monthly subscription charge, which allows them to stay online as long as they wish.
The service will have the added advantage of offering Internet access at up to 40-times the speed of conventional telephone modems by using Telewest's local cable network.
Tony Illsley, Telewest's new chief executive, is thought to be impressed with the success of similar US products such as Road Runner and At Home Networks.
Both services, which have signed up hundreds of thousands of users, offer high-speed Internet access for a flat monthly fee.
Telewest's move will increase the pressure on Internet service providers such as Freeserve, the service launched by Dixons, to cut their call charges.
Free Internet service providers have taken the market by storm in the past six months by abandoning monthly subscription charges. But users still have to pay local call charges for each minute they spend online.
Last week Oftel, the telecoms watchdog, challenged existing service providers to offer cheaper call rates. British Telecom is currently adapting its billing system to allow service providers to subsidise the cost of calls.
Meanwhile, X-Stream, the innovative service provider which pioneered the Freeserve model a year ago, is currently experimenting with a totally free service.
Each weekend this month the service, which makes money by streaming advertising along the bottom of its Internet browser software, is offering users the chance to access the Internet for nothing by dialling up through an 0800 number.