Deloitte, which took control of HMV on Tuesday, said on Wednesday Blockbuster's 528 stores would continue to trade as normal in the meantime.
Blockbuster, which employs 4,190 staff and is owned by U.S. satellite TV company Dish Network, is the third casualty in Britain's retail sector in the Christmas aftermath, with many specialist shops struggling against competition from supermarkets like Tesco, online retailers like Amazon and download sites like Apple's iTunes.
The retail sector has also been pressured by muted wage growth among its customers and by government austerity measures squeezing household budgets.
Camera specialist Jessops went into administration last week and said it will close all 187 of its stores resulting in 1,370 job losses.
But the move into administration on Monday of HMV, the 92-year old music retailer, has arguably struck the biggest blow to town centers.
Blockbuster, which rents DVDs and video games, opened its first store in the UK in March 1989. It launched an online service in 2002, but the DVD rental model became obsolete in the face of online rental subscription services such as Amazon's LoveFilm and digital streaming.
Dish Network Corp, the second-largest U.S. satellite TV company, bought the failed Blockbuster LLC video rental chain in a bankruptcy auction in 2010.
Deloitte's Lee Manning said the firm would be working closely with suppliers and employees to secure a sale, preserve jobs and generate as much value as possible for creditors.
(Reporting by Lorraine Turner and Neil Maidment; Editing Kate Holton and David Holmes)
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