Byline Media and its co-director Peter Jukes have demanded an apology and damages from two leading Brexit campaign figures over claims Sunday Times political editor Isabel Oakeshott’s emails were hacked.

Leave.EU donor Arron Banks and director of communications Andy Wigmore have repeatedly alleged that Byline, Jukes and Observer journalist Carole Cadwalladr had obtained hacked or stolen documents as the source of their story published this weekend detailing Banks’s links to Russian officials.

Both journalists have repeatedly denied the allegations on Twitter.  Cadwalladr told Press Gazette yesterday: “We had received some material that we knew came from a perfectly legitimate source and it was somebody who thought that it desperately had to be out in the public domain.”

A Guardian News and Media spokesperson told Press Gazette today it is not currently pursuing any accompanying legal action but is monitoring the situation. “GNM stands by its reporting,” they added.

After Banks and Wigmore repeated the allegation numerous times on Twitter between Saturday and yesterday, Bindmans law firm last night wrote on behalf of Byline and Jukes (pictured) to Mishcon de Reya under pre-action protocol for defamation.

The legal letter states that they obtained the information for publication, including copies of Banks’s emails, from a confidential source who had obtained the emails “entirely lawfully” in November last year.

The letter said: “For the avoidance of doubt we should also make it absolutely clear to your clients that the allegation that our clients knowingly received hacked or stolen information is also false.

“As journalists, there are obviously times when it is appropriate to publish information that was originally obtained unlawfully. However, this is not what happened.”

The letter pointed to a number of tweets in particular, including Banks saying on Saturday that the Observer’s story was obtained from emails stolen from Oakeshott, and Wigmore retweeting it and adding: “Hacked emails tut tut.”

On Sunday Banks tweeted that he was told by Oakeshott that her emails were hacked by Byline and the Guardian and that they were using stolen information.

Oakeshott has posted a screenshot of an email proving that her Dropbox account was improperly accessed but Byline’s lawyers said they had nothing to do with any attempt to access this account.

“They did not steal any information from anyone,” the letter said.

“They were assured, and believe, that the information they received was not accessed unlawfully and the circumstances in which it was provided to them (which are confidential) support that belief.

“They were presented with material of potentially immense public importance, which had a clear provenance, and they therefore published it.”

Byline said that the allegations of hacking, or commissioning others to hack or steal on their behalf, would be an exceptionally serious offence under the Computer Misuse Act 1990 and/or the Theft Act, and therefore reached the serious harm threshold under the Defamation Act 2013.

They also claimed the repeated tweeting of false allegations was an “intimidatory tactic, designed to cause our clients alarm and distress”, making it a breach of the Protection from Harassment Act 1999.

Byline and Jukes requested that Banks and Wigmore publish a retraction and apology in terms to be agreed; pay a sum in damages; compensate them for legal costs; and agree not to repeat the allegations any further.

“Should you agree to these steps, our clients will take the matter no further,” the letter said.

“If not, our clients reserve the right to issue proceedings against yours with no further notice.”

They also said the relevant tweets should be removed immediately, with a retraction published.

Mishcon de Reya has not responded to requests for comment.

But after Byline tweeted to say that a solicitor’s letter was on its way, Banks responded: “Hold on, I thought you believed in freedom and transparency Carole Cadwalladr and not hiding behind lawyers, no ?”

The Observer’s Cambridge Analytica whistleblower Christopher Wylie has also denied any involvement in illegally obtaining the documents.

Wyle said on Twitter today: “To be clear, I did not steal ‘hacked’ emails from Arron Banks.

“I was shown them and I then reported Mr Banks and Mr Wigmore to the authorities because it was concerning that Leave.EU officials were in discussions about Brexit and large financial deals with the Russian ambassador.”