The attacks did not lead to any data breach as, according to the party, its "robust" security system foiled the attempt to disrupt the functioning of the party's digital systems, the BBC reported on Tuesday.
In a letter sent to Labour campaigners, Niall Sookoo, the party's executive director of elections and campaigns, said: "Yesterday afternoon our security systems identified that, in a very short period of time, there were large-scale and sophisticated attacks on Labour Party platforms which had the intention of taking our systems entirely offline.
"Every single one of these attempts failed due to our robust security systems and the integrity of all our platforms and data was maintained."
The attack was a "real concern", Labour's General Secretary Jennie Formby said on Twitter.
Reports suggest that it was just a Distributed Denial of Service (DDoS) attack which floods a computer server with traffic to try to take it offline.
DDoS attacks are not normally recognised as being a hack as they do not involve breaking into a target's systems to insert malware, said the BBC report, adding that Labour is using software by the technology company Cloudflare to protect its systems.
"We have experienced a sophisticated and large-scale cyber-attack on Labour digital platforms. We took swift action and these attempts failed due to our robust security systems. The integrity of all our platforms was maintained and we are confident that no data breach occurred," a spokeswoman of Jeremy Corbyn's party was quoted as saying by The Register.
"Our security procedures have slowed down some of our campaign activities, but these were restored this morning and we are back up to full speed. We have reported the matter to the National Cyber Security Centre."
( With inputs from IANS )