This suspension occurred at around 09:15 BST.
The problems came after the LSE experienced a very busy morning of trading, with the flagship FTSE 100 index rising strongly to 5,440.
This is mainly due to news of the US government's bailout of giant mortgage lenders Fannie Mae and Freddie Mac, in order to provide the firms' borrowers with additional security.
A spokesperson for the exchange said that staff were "currently preparing" to reconnect the system in a "controlled way", before the suspension was lifted at around 11:45 BST.
However, the BBC reports that trades cannot yet be executed on the system, although entering or deleting share trades has been enabled.
Speaking to Bloomberg, Sejal Patel, a London-based trader at CMC Markets, commented: "Today's meltdown from the LSE couldn't have come at a worse time."
He added: "It has served to highlight the benefits of having an additional exchange."
The computer glitch has caused the longest disruption of trading on the LSE for eight years.