Telewest Broadband claims that 5,000 of its subscribers have upgraded to a 1Mbps connection within a week of its launch.
The IMbps service costs £10 per month more than Telewest's 512Kbps Blueyonder broadband access service.
Around three per cent of the cable firm's 170,000 broadband subscribers are said to have already opted to pay the extra.
The 1Mbps connection costs £35 per month when taken with other Telewest broadband services, or £39.99 on its own plus a £50 installation fee.
Cable has held a long-standing price advantage over BT-supplied ADSL lines sold through internet service providers, although the gap has closed over recent months following price cuts by BT.
Telwest says demand for the 1Mbps product would be driven by a growing number of websites providing top-speed content, such as highly-encoded video and mega-sized files.
"We have been confident there is good demand for a further bandwidth boost, but consumer enthusiasm has been even better than we anticipated. It seems Blueyonder customers definitely want to go faster!" said Chad Raube, head of internet services at Telewest Broadband.
The cable operator also has more than 300,000 dial-up internet customers who have yet to upgrade to the faster service.
Cotton seedling freezes to death as Chang'e-4 shuts down for the Moon's 14-day lunar night
Fortnite easily out-earns PUBG, Assassin's Creed Odyssey and Red Dead Redemption 2 in 2018
Meteor showers as a service will be visible for about 100 kilometres in all directions
Saturn's rings only formed in the past 100 million years, suggests analysis of Cassini space probe data
New findings contradict conventional belief that Saturn's rings were formed along with the planet about 4.5 billion years ago