Tim Mason, Tesco's marketing director says: "We are excited about the results in Osterley. We want to find out if that is something special to that area or if it can be replicated elsewhere."
Tesco claims that the Osterley trial has attracted hundreds of devotees with the average purchase double that achieved in a regular store.
Half of the customers have been ordering via phone or fax. The remainder have been ordering through the Internet option, a higher proportion than expected.
"We're really pleased with the response from customers," Tesco said. "People are ordering across the product range, not just the staple products, but fresh meat, fruit and vegetables too."
Tesco launched its Internet shopping trial last October, offering the service to holders of its Clubcard loyalty scheme. Customers can choose from 20,000 product lines, the same as in a normal store. They pay a pounds 5 fee for delivery.
Tesco is the most advanced of the big supermarkets in home shopping. Sainsbury's is also conducting trials and has links with a home delivery company in south London called Flanagan's. Tesco's Tim Mason said the aim was to help customers to shop "without the physical effort of shopping".
Users of the Tesco service say it can take up to two hours to place the first order as the system is unfamiliar. After that the process may take only 15 minutes.