According to the Mail on Sunday, hacker group Anonymous carried out the attack on Thursday morning.
The group claims the attack on the London Stock Exchange was the latest in a series that has also seen it target the websites of NYSE Euronext and the Turkey Stock Exchange as part of a campaign called Op Icarus.
A spokesman for the London Stock Exchange did not respond to request for comment.
It comes days after Time Inc confirmed that social network Myspace had fallen victim to a cyber attack.
The firm said it believed the attack originate in Russia, and compromised usernames, passwords and email addresses, from the old Myspace platform prior to 11 June, 2013 - the date that the social network was relaunched with "significant steps" taken to strengthen security.
As Myspace does not collect users' credit card details, no financial information was leaked in the hack.