Theresa May must launch an independent investigation into “foreign influence and voter manipulation” in the Brexit vote, a committee of MPs says today, amid growing evidence of lawbreaking by Leave campaigners.

A highly critical report – which warns “democracy is at risk” from rogue practices on social media – turns its fire on the prime minister for the failure to probe their effect on the referendum result.

But Downing Street has fought off calls for a “Mueller-style” inquiry, on the scale of the US probe into alleged collusion with Russia by Donald Trump’s presidential campaign.

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Now the Digital, Culture, Media and Sport Committee has insisted an inquiry must be carried out, also looking into the 2017 general election and the 2014 Scottish referendum.

It would establish “what actually happened with regard to foreign influence, disinformation, funding, voter manipulation, and the sharing of data, so that appropriate changes to the law can be made and lessons can be learnt for future elections and referenda”.

Damian Collins, the committee’s Conservative chair, urged the prime minister to come clean about whether “Russian interference in UK politics” was being probed.

“We want to find out what was the impact of disinformation and voter manipulation on past elections including the UK referendum in 2016, and are calling on the government to launch an independent investigation,” he said.

The call comes in a hard-hitting report into so-called fake news, which also:

* demands an independent regulator with the power to prosecute social media companies that fail to tackle “harmful or illegal content”.

* calls for tougher “rules on overseas involvement in UK elections” and electoral communications laws.

* demands a requirement on social media companies to take down “proven sources of disinformation”.

* brands electoral law “not fit for purpose” because it fails to cope with “microtargeted” online political campaigning.

* finds Facebook “intentionally and knowingly violated both data privacy and anti-competition laws”.

* calls for its “use of users’ and users’ friends’ data” to be fully investigated.

* attacks Facebook chief Mark Zuckerberg for his “contempt” in refusing to appear before the committee last year.

Mr Collins added: “Democracy is at risk from the malicious and relentless targeting of citizens with disinformation and personalised ‘dark adverts’ from unidentifiable sources, delivered through the major social media platforms we use every day.

“Much of this is directed from agencies working in foreign countries, including Russia.”

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The crisis emerged after the Brexit referendum, leading to the finding against Vote Leave which has been referred to the police for busting spending limits

Crucially, the cash was used to pay data firm Aggregate IQ and – a whistleblower and an Oxford professor argue – potentially enabled it to precisely target enough voters on social media to have swayed the Brexit result.

Mr Banks, Nigel Farage’s ally, could receive a two-year prison sentence if he is found to have “knowingly concealed” that an Isle of Man company handed up to £8m to Leave.EU – which would have been outlawed as a foreign donation.

However, Ms May has repeatedly downplayed the commission’s findings – even though they were to a “criminal standard of proof” – and has hailed the referendum as “a great exercise in democracy”.

Only three of 42 recommendations in the committee’s interim report last year were accepted, in a response that ducked pressure for an independent investigation entirely.

Earlier this month, the commission asked the government for beefed-up powers to prosecute parties and campaigners, to keep pace with social media, a call backed by the committee.