The chain, which has 528 stores has appointed accountancy firm, Deloitte, which will now take over the running of the firm. It has said Blockbuster UK would keep trading while it tries to find a buyer.
Earlier this month retailer HMV and photographic supplies retailer Jessops both went into administration.
Glyn Mummery at the insolvency specialist, FRP Advisory, said: "This has been the worst Christmas period on the high street in living memory.
"The new age of online retailing has caused a bloodbath in the electronics and entertainment markets for old-school retailers."
Lee Manning, a partner in Deloitte's restructuring services practice, said: "We are working closely with Blockbuster's suppliers and employees to ensure the business has the best possible platform to secure a sale, preserve jobs and generate as much value as possible for all creditors.
"The core of the business is still profitable and we will continue to trade as normal in both retail and rental while we seek a buyer for all or parts of the business as a going concern."
Manning added: "During this time gift cards and credit acquired through Blockbuster's trade-in scheme will be honoured towards the purchase of goods."