After Saturday's deadly London terror attack, British Prime Minister Theresa May said technology companies need to do more to stop terrorists from working together online.

"We cannot allow this ideology the safe space it needs to breed. Yet that is precisely what the internet and the big companies that provide internet-based services provide," May said Sunday. "We need to work with allied democratic governments to reach international agreements that regulate cyberspace to prevent the spread of extremism and terrorism planning."

CBS News senior national security analyst Fran Townsend, who was President George W. Bush's homeland security adviser, agreed, calling cyberspace the "single most important component right now" in addressing terror.

"Let's remember, using the Telegram channel, the encrypting messaging application, ISIS called for Ramadan attacks using cars, knives and guns. And we've seen this incredible rise in these Ramadan attacks right now. And so I think what Theresa May is trying say is we need to battle the cyberspace just as you would the physical space – air, sea, land. We need to approach it in that way to confront them, deny them the use of the internet," Townsend said Monday on "CBS This Morning"

While Twitter suspended 376,890 accounts in 2016, Townsend said tech companies need to do more.

"[Twitter was] very late to the game and had to be sort of shamed into doing it. They have an understandable and righteous concern about First Amendment. I get that. By the same token, you can't allow yourselves to provide – these social media companies – material support, right? That's a criminal offense, to provide material support," Townsend said. "And so you have to do more. They have to deploy technology that will allow them to identify video, audio, pictures and take them down."

But videos spreading the message of extremism still exist online. Townsend gave the example of Anwar al-Awlaki, the American-born al Qaeda cleric who was killed by a drone during the Obama administration.

"If you go online right now and you Google him, you can bring up his sermons, and so that stuff's still online and he's permitted to terrorize us from the grave," Townsend said.

Seven people were killed in Saturday's van and knife attack on London Bridge and Borough Market, and at least 48 people, including two Americans, were injured. ISIS claimed responsibility for the attacks. Investigators have carried out a series of raids and are detaining people, looking for connections to the attackers. Over the weekend, British police arrested 12 people in east London, and one was later released.

This was Britain's third terror attack since March.