SNP Westminster leader Ian Blackford has pressed Theresa May on whether the UK Government has any connections to the parent company of the data firm Cambridge Analytica (CA) – as he outline a series of links between SCL and the Conservative Party.

CA is facing questions over whether it used data from millions Facebook users' accounts to sway the outcome of the US 2016 presidential election and the Brexit referendum.

Speaking in the House of Commons, the SNP's Westminster leader said: "Can I point out to her that the parent company of Cambridge Analytica, the strategic communications laboratories has been run by a chairman of Oxford Conservative Association, it's founding chairman was a former Conservative MP ... a former Conservative Party treasurer is a shareholder. We know that the links to the Conservative Party go on and on. Will the Prime Minister tell us of her government's connections to the company?"

May responded that "as far I'm aware the Government has no current contracts with Cambridge Analytic or with the SCL group."

She added the allegations surrounding Cambridge Analytica were "very concerning" and "it was right that they should be investigated". She asked Facebook to comply fully in the inquiry, launched on Monday by the UK Information Commissioner.

After Blackford's question, the Green MP Caroline Lucas posted a link to a newspaper article from December 2016 which reported Tory chiefs were in talks with Cambridge Analytica, in a bid to recruit the firm to help in its next election campaign.

Lucas tweeted: "The Prime Minister says the Govt has no current contracts with Cambridge Analytica or SCL. But what about past deals?"

Earlier today the researcher who developed an app used by Cambridge Analytica to harvest millions of Facebook users' data claimed he has been made a "scapegoat" in the row.

Dr Aleksandr Kogan told BBC Radio 4's Today programme that CA approached him to do the work – rather than the other way around – and insisted he believed it was above board.

"What happened was they approached me. In terms of the usage of Facebook data they wrote the terms of service for the app, they provided the legal advice that this was all appropriate," he said.

Dr Kogan said he regretted not asking more questions about the work he did for CA.

"One of the great mistakes I did here was I just didn't ask enough questions," he said.

"I had never done a commercial project, I didn't really have any reason to doubt their sincerity.

"That's certainly something I strongly regret now."

He added: "My motivation was to get a dataset I could do research on; I have never profited from this in any way personally."

Dr Kogan said CA's suspended chief executive Alexander Nix was wrong when he told MPs he had not been supplied data by the academic's firm GSR.

Nix told MPs that GSR "did some research for us back in 2014" that "proved to be fruitless".

Asked if that was wrong, Dr Kogan said: "I believe it is. I don't see why that would be accurate."

Dr Kogan said he would be prepared to appear before MPs or the US Congress to give his version of events.

Prime Minister Theresa May told the House of Commons: "What we have seen in Cambridge Analytica, the allegations are clearly very concerning. It is absolutely right that they should be properly investigated.

"It's right that the Information Commissioner is doing exactly that, because people need to have confidence in how their personal data is being used.

"I would expect Facebook, Cambridge Analytica and all organisations involved to comply fully with the investigation that is taking place.

"I'm pleased to say that the bill we are bringing forward on data protection will strengthen legislation around data protection and give the Information Commissioner's Office tougher powers to ensure organisations comply, and I would hope it would be supported from everybody across this House."

The backlash against Facebook over its handling of personal data has seen calls for users to delete their profiles and wiped billions of dollars off the social media giant's market value.

Damian Collins, chairman of the Digital, Culture, Media and Sport Committee, wrote to Facebook founder Mark Zuckerberg yesterday requesting that the firm explains the "catastrophic" failure.

CA suspended Nix on Tuesday, after recordings emerged of him making a series of controversial claims, including boasts that CA had a pivotal role in the election of Trump.

The CA board said that Nix had been suspended "with immediate effect, pending a full, independent investigation".

Facebook and Cambridge Analytica both deny any wrongdoing.