The deputy Labour leader demanded a 'Mueller-style' probe – referring to the FBI investigation led by Special counsel Robert Mueller into Russian links to Donald Trump's presidential campaign – to see if the Kremlin 'stole' the 2016 vote.
Speaking during Culture Questions, the West Bromwich East MP and shadow culture secretary said it was clear that Facebook had broken the law and allowed illegal data breaches during the referendum.
He said: "Isn't it now the time, in the public interest and in the national interest, to have a Mueller-style inquiry into the conduct of the EU referendum, that also examines the role played by the Russian state?"
Digital Minister Margot James, the MP for Stourbridge, said in response: "There's no doubt that the law as it stands has been updated; the Information Commissioner's Office has much increased powers and will be encouraged to use them.
"There's no doubt these serious matters concerning the European referendum will be investigated but it's really not a matter for my department."
Downing Street said the issue was one for the Electoral Commission to deal with. However, Mr Watson has previously said the commission was clearly not the right the body to be tasked with investigating state interference.
At a recent Q&A session at the Byline Festival Mr Watson suggested the vote may have been 'stolen'. He said that if the National Crime Agency was not investigating the issue, then a full public inquiry must be held.
“There’s half a dozen different bodies looking at different aspects of this and I just don’t think this is the way for the British people will get the truth of what happened," he said. "I really do think we need a Mueller-style inquiry to establish the facts and there’s obviously an urgency to this.”
Ben Bradshaw, the Labour MP for Exeter, has been pressing for the past 18 months for the Government to act on reports of Russian interference.