The announcement comes after Amazon said it would buy a British streaming firm. Inc. today launched a service that enables its Amazon Prime customers to instantly stream more than 5,000 movies and television shows, and to watch them without commercials.

Consumers who pay $79 annually for Amazon Prime receive unlimited two-day shipping on products without minimum purchase amounts. The streaming offer follows the announcement last month by Amazon, No. 1 in the Internet Retailer Top 500 Guide, that it would buy LoveFilm, a U.K.-based video rental and streaming company with 2009 sales of about $158.8 million. LoveFilm has 1.6 million subscribers in Europe.  Amazon has not said how many consumers subscribe to Amazon Prime, but  Colin Sebastian, an analyst at Lazard Capital, has put the number at 6 million.

“Adding unlimited instant access to thousands of movies and TV shows at no additional cost is a great way to give members even more value for their $79 annual Amazon Prime membership,” says Robbie Schwietzer, vice president of Amazon Prime.

Amazon Prime faces stiffening competition from retailers and groups of retailers who are imitating the model of offering unlimited free shipping for a set annual fee. Among the most notable competitors is ShopRunner, a free-shipping program operated by e-commerce services firm GSI Commerce Inc. that has signed up more than 60 merchants.