The jobs of 4,190 staff throughout 528 stores nationwide are now at risk - including those working at stores in Reading.
Deloitte has been appointed as the firm's administrators and say that all stores will operate as normal while it hunts for a buyer.
Lee Manning, spokesman for the accountancy firm, said: "In recent years Blockbuster has faced increased competition from internet-based providers along with the shift to digital streaming of movies and games.
"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."
He added that gift cards and credit acquired through Blockbuster's trade-in scheme will be honoured.
The American company launched in the UK in 1989, and while initially successful, has struggled to compete with online services such as Netflix and LoveFilm in recent years.
This comes after music and film giant HMV announced the same news on Monday and camera company Jessops last week.