A Labour MP has asked Theresa May whether she or any other minister had ever declined a request from the security services to conduct an investigation into the controversial Leave.EU campaign donor Arron Banks.

Ben Bradshaw wrote to the prime minister a day after it was announced that a criminal investigation into Banks had begun, amid repeated allegations that May had blocked an investigation in 2016, when she was home secretary.

Bradshaw said the allegation was extremely serious. “I have today written to the prime minister to ask if she or any other minister or senior official has at any stage declined a request from any of our security, intelligence or law enforcement agencies to investigate Banks,” he said.

On Thursday, the Electoral Commission concluded that there were reasonable grounds to suspect Banks was “not the true source” of donations totalling £8mto the Leave.EU campaign.

The elections watchdog also referred Banks and Leave.EU to the National Crime Agency, which said it would begin an investigation on the grounds that “a number of criminal offences may have been committed”.

Banks denies any wrongdoing. “I am a UK taxpayer and I have never received any foreign donations”, he said on Thursday.

Liz Bilney, a Banks associate who is also under investigation, added: “I run the group of companies where the money was from and we don’t have any transactions that are from Russia.”

Downing Street would not comment on Bradshaw’s suggestion that an investigation was blocked, although it is understood the claim is denied. A No 10 spokesman said: “We would never confirm or deny the detail of any conversation with security services on any topic.”

The Daily Mail reported on Thursday that May declined a request by one of the security services to investigate Banks in 2016, repeating a claim made by Tom Watson, Labour’s deputy leader, at his party conference in September.

At the time Watson asked: “Did [May] ask the security services to investigate? Or did she stop them doing so? There is a suggestion that in the run-up to the referendum the prime minister – in her capacity at the time as home secretary – declined at least one application from the security services to mount a full investigation into Mr Banks and others suspected of Russian influence. We need to know if that is true.”

The Electoral Commission concluded that Banks was not the true source of the £8m in funds provided to the Leave.EU referendum campaigns; that the funding involved a non-qualifying or impermissible company – Rock Holdings Ltd – based in the Isle of Man; and that Banks, Bilney and others concealed the true details of the financial transactions.

Banks has been invited to appear on the BBC’s The Andrew Marr Show this weekend, where he is expected to respond again to the allegations. He told the Times he had obtained a legal opinion, which he would refer to on air, to show that lending money via Rock Holdings was legitimate.