A group calling itself New World Hacking said that the attack reached 602Gbps. If accurate, that would put it at almost twice the size of the previous record of 334Gbps, recorded by Arbor Networks last year.
"Some of this information still needs to be confirmed," said Paul Nicholson, director of product marketing at A10 Networks</a>, a security vendor that helps protect companies against DDoS attacks.
"If it's proven, it would be the largest attack on record. But it depends on whether it's actually confirmed, because it's still a relatively recent attack."
According to Nicholson, it sometimes happens that people who step forward and take credit for attacks turn out to be exaggerating.
New World Hacking also said that the attack, which came on New Year's Eve, was "only a test."
"We didn't exactly plan to take it down for multiple hours," the group told the BBC. New World Hacking also hit Donald Trump's campaign website the same day, and said its main focus was to take down ISIS-affiliated websites.
It's common for hackers to go after high-profile media websites, but attacks against political websites are increasingly likely to be in the spotlight this year because of the U.S. election cycle, according to Raytheon|Websense CEO John McCormack.
"The U.S. elections cycle will drive significant themed attacks," he said. "This is just the beginning and it will get worse -- and more personal -- as candidates see their campaign apps hacked, Twitter feeds hijacked, and voters are targeted with very specific phishing attacks based on public data such as voter registration, Facebook and LinkedIn."
One possible reason to conduct a DDoS attack against a high-profile target such as the BBC or Donald Trump is marketing, said A10 Networks' Nicholson.
It seems that New World Hacking may be affiliated with an online DDoS tool called BangStresser, which delivers attacks as a service.
Last year, a similar group, the Lizard Squad, conducted a marketing campaign for their DDoS service, the Lizard Stressor.
"There are a lot of parallels here," said A10 Networks' product marketing manager Rene Paap.
These services typically leverage botnets or use stolen payment cards to rent cloud-based servers, he said. Typically, the rented servers are used to run command and control servers.
What's unusual about New World Hacking is that they're claiming to be using Amazon servers to generate actual attack bandwidth.
"That is something new," said Paap. "But it hasn't been confirmed or denied yet."
Not all DDoS attack services are illegal, said Nicholson.
"Some are offered as useful services to websites, to see if they can handle the load," he said.
Others fall squarely into the gray area, allowing cyber-terrorists, extortionists and digital vandals to launch attacks for a few hundred dollars each.
"Some of them are quite inexpensive and configurable," Nicholson said. "for example, you can have different attacks at different times, so that it's harder to defend against them."
To protect themselves, Nicholson recommends that companies deploy a combination of on-premises and cloud-based solutions to handle attacks of varying types and sizes.
"You need to be able to detect what's going on, that there's actually an attack," he said. "And once you detect an attack, you need to be able to mitigate it as long as possible."
According to security vendor Netcraft, service to the BBC network was restored by using the Akamai content delivery network.
Akamai declined to comment about this particular case. "As policy, the company isn't commenting on specific situations," said a spokesperson.