Mr Banks, who founded and bankrolled the Leave.EU campaign, said that his “personal data” had been illegally obtained and distributed in posts on the account.
A furious Mr Banks accused Twitter of “deliberately allowing” the hacked messages to remain in the public domain for hours after he informed the tech giant that his account had been compromised.
Spokesman Andy Wigmore said that the insurance tycoon was ready to take legal action under the Computer Misuse Act against anyone who had downloaded messages.
The data was made available in the form of a link to a download file, which is no longer online.
Soon after its appearance, a number of what appeared to be direct messages between the Leave.EU chief and various public figures were circulating on social media, though it appeared that at least some of these were fakes created after the initial hack took place.
A source close to foreign secretary Dominic Raab told The Independent that a message bearing the signature “raab” was a fake and had not been sent by the cabinet minister.
The Twitter feed @WhitePings released a statement claiming to be behind the hack, stating that it had been carried out “to signify all the hateful comments he had made, nothing more”.
In a statement released by Leave.EU, Mr Banks said: “I became aware last night that my Twitter account had been hacked and that persons involved have posted personal data obtained illegally via Twitter.
“The matter has been reported to the police.
“Twitter were notified 12 hours ago and despite repeated requests they have not taken action to deactivate the account or remove the illegal data downloads. Despite the obvious lack of security at Twitter relating to personal data, they have deliberately chosen to leave personal data in the public domain.”
In February 2019, Leave.EU and an insurance company owned by Mr Banks were fined £120,000 by the Information Commissioner’s Office for breaching data protection laws.
In a statement, Twitter said: “We have taken steps to secure the compromised account. We will continue to take firm enforcement action in line with our policy which strictly prohibits the distribution on our service of materials obtained through hacking.”