His comments were made at an event organised by the Times newspaper.
The NCSC was established about a year ago. Last month, it revealed that it had already classed a total of 590 attacks – from a variety of perpetrators – as being “significant”, and that more than 30 incidents had been judged serious enough to require a cross-government response.
The NCSC chief referenced this in his own speech.
“The prime minister made the point on Monday night – international order as we know it is in danger of being eroded,” he said.
“This is clearly a cause for concern and the NCSC is actively engaging with international partners, industry and civil society to tackle this threat.”
Many were in favour of the UK leaving the European Union, but a minority were pro-Remain. The academics involved believed the posts were seen hundreds of millions of times.
“Ukraine experienced [a similar] information war in 2014 – and if it worked in Ukraine it can also work in Western democracies,” said Prof Sasha Talavera from Swansea University.
“One can use it to split society and marginalise groups. Social media nowadays is a powerful tool.”
He added that some form of regulation of the large social media firms might now be required.
The Guardian reports details of a separate University of Edinburgh study that also presents evidence of Russia using Twitter to sway opinion in the lead-up to the Brexit vote.
The Kremlin has previously denied trying to meddle in the referendum.
But the chairman of the Commons Digital, Culture, Media and Sport Select Committee, Damian Collins, said he now wanted Twitter to share examples of tweets linked to a Russian “troll factory”, known as the Internet Research Agency, about British politics.