In this case, Spamhaus's Domain Name System (DNS) servers were targeted - the infrastructure that joins domain names, such as bbc.co.uk, the website's numerical internet protocol address.
Mr Linford said the attack's power would be strong enough to take down government internet infrastructure.
"If you aimed this at Downing Street they would be down instantly," he said. "They would be completely off the internet."
He added: "These attacks are peaking at 300 gb/s (gigabits per second).
"Normally when there are attacks against major banks, we're talking about 50 gb/s."