The movies and games rental chain's 528 outlets are now under threat, with a potential 4,190 jobs that could be lost.
Administrator Deloitte is seeking a buyer for the company, which will continue to accept gift cards during the process.
Lee Manning from Deloitte's Restructuring Services practice said: "We are working closely with 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 whilst we seek a buyer for all or parts of the business as a going concern.
"During this time gift cards and credit acquired through Blockbuster's trade-in scheme will be honoured towards the purchase of goods."
The first Blockbuster store in the UK opened in March 1989 in London. The company now claims to be the UK's largest DVDs and video games rental service.
The news follows entertainment chain HMV calling in the administrators earlier this week.
The music, video and game retailer had been criticised for refusing to honour gift cards and vouchers while in administration.