THERESA May has been urged to “come clean” by the SNP over claims of improper spending during the EU referendum campaign.

During Prime Minister’s Questions, the Prime Minister was challenged by Ian Blackford, the Nationalist leader, who claimed that the "shady business" of data mining and undermining electoral law went “right to the heart" of the Tory Party.

The Prime Minister made clear it was "right" that allegations were investigated by the Electoral Commission, the elections watchdog, adding that "if there are allegations of criminal activity that should be taken to the police".

Mr Blackford, the MP for Ross, Skye and Lochaber asked: "The public must have trust in our political process.

"Does the Prime Minister agree with me that transparency in political campaign spending and the integrity of electoral laws across the UK must be upheld?

"Will the Prime Minister join with me in saying that all allegations of improper spending during the EU referendum must be fully investigated?"

Mrs May responded: "We have laws about election spending that parties are required to abide by.

"I understand that any allegations that have come forward in respect of spending during the referendum have already been investigated by the Electoral Commission, but of course it's right that allegations are investigated by the Electoral Commission."

Mr Blackford then called on the PM to issue details of transactions between certain pro-Brexit groups.

He told MPs: "We know that before the EU referendum the DUP received £425,000 from the Conservative-run Constitutional Research Council[CRC] chaired by Richard Cook, former Vice-Chair of the Scottish Tories. We know some of the money was given to AggregateIQ, a reported franchise of Cambridge Analytica[CA].

"We know that[former CA employee and whistle-blower] Chris Wylie is absolutely convinced of a common purpose between Vote Leave, BeLeave, Veterans for Britain and the DUP.

"The shady business of data mining and undermining electoral law goes right to the heart of the Prime Minister's party. Will the Prime Minister issue the full details of the transactions between the DUP and the Scottish Tory-linked CRC?"

Mrs May replied: "I understand that this is a matter that has already been investigated twice by the Electoral Commission and he raises questions about inquiries.

"If there are allegations of criminal activity that should be taken to the police. The regulator of election spending is the Electoral Commission so if there's an allegation of breaches of campaign spending, or campaign funding rules then this should be taken by the Electoral Commission.

"My understanding is the Electoral Commission does indeed investigate these and will continue to do so when allegations are brought to its attention," she added.

Later, Mr Blackford called on the Tory leadership for full disclosure. “They have got to come clean. We need to have transparency. People need to have faith in politics and there is genuine concern and I credit the media in the interest they have shown in this subject over the course of the last four weeks because it goes to the very heart of what our democracy is about.”

He added: “All of us have a responsibility to ensure we are shining a light on this and the Government and the Conservative Party have questions to answer.”

Meanwhile, MPs have given Facebook founder Mark Zuckerberg a 12-day deadline to rethink his refusal to answer their questions on fake news.

His rejection of an invitation to appear before the House of Commons Digital, Culture, Media and Sport Committee was branded "absolutely astonishing" by chairman Damian Collins.

He has now written to Facebook insisting Mr Zuckerberg is "the right person" to give evidence to the inquiry and demanding an answer by April 9.

The billionaire social media tycoon said on Tuesday he was ready to appear before the US Congress amid growing furore over the alleged misuse of Facebook users' personal information by CA to target campaign ads during Donald Trump's successful bid for the presidency.

The Culture Committee also announced the suspended CA chief executive, Christopher Nix, would return to give evidence for a second time on April 17.

On his first appearance in February, Mr Nix denied the company had been involved in the 2016 EU referendum and insisted it did not use Facebook data.

But his evidence was branded "exceptionally misleading" in explosive testimony to the committee on Tuesday by Mr Wylie.