It comes after the whistleblower behind allegations about the misuse of Facebook users' data told MPs he is 'absolutely convinced' that 'totally illegal' co-ordination helped win the 2016 referendum for the Leave campaign.
At Prime Minister's Questions, the SNP's Westminster leader Ian Blackford said "all allegations of improper spending during the EU referendum must be fully investigated". He will write to Theresa May asking for her to support a probe by the Electoral Commission and calling on her to issue details of transactions between certain pro-Brexit groups, Mr Blackford confirmed later.
Vote Leave passed Â£675,000 on to BeLeave, a group set up by fashion student Darren Grimes, 22. Almost all the money was then spent on hiring AggregateIQ (AIQ) to target advertising at web users.
Vote Leave also spent 40 per cent of its budget with AIQ.'¨A further Â£32,000 was paid to AIQ by the DUP after receiving Â£425,000 from the Constitutional Research Council, chaired by Richard Cook, a former vice-chairman of the Scottish Conservatives.
Read more at: https://www.scotsman.com/news/politics/illegal-co-ordination-won-brexit-vote-claims-whistleblower-1-4713958
In the Commons, the SNP MP 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 added: "We know that before the EU referendum the DUP received Â£425,000 from the Conservative-run Constitutional Research Council (CRC)... we know some of the money was given to AggregateIQ a reported franchise of Cambridge Analytica.
"We know that 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."