Arron Banks ordered his Leave.EU campaign group to continue promoting pro-Brexit adverts in the wake of the murder of Jo Cox, despite an agreement to suspend campaigning, according to Channel 4 News.

Immediately after the MP’s killing, politicians on both sides of the EU referendum debate agreed to the suspension, and remain and leave campaigners cancelled speeches and events.

However Channel 4 News said it had seen email sent the morning after Cox’s murder from Banks, Leave.EU’s key financial backer, to his assistant Liz Bilney, the campaign group’s chief executive, that read: “Keep pumping the McKenna video” and “up the Spend A”.

The campaign had enlisted the TV hypnotist Paul McKenna to advise on its broadcasts. Bilney replied to Banks: “Yes that’s starting to get traction now and with paid advertising and no active campaigning could get a lot of take up today.” Banks responded: “Exactly – press it harder.”

Cox, a Labour MP for the Batley and Spen constituency in West Yorkshire, was murdered by a far-right terrorist in 2016, one week before the EU referendum. Her killer was sentenced to life in prison.

Channel 4 News also accused Banks of secretly funding other pro-Brexit campaigners, potentially contravening electoral law.

The insurance businessman is under investigation by the National Crime Agency after the Electoral Commission said it could not be certain he was the true source of millions of pounds of funding for the Brexit campaign.

The programme also alleged that internal emails indicated that a Leave.EU staffer drafted a press release for the Labour Leave campaign accusing media organisations of politicising Cox’s killing. It said Labour Leave later disavowed the press release and said it had been falsely issued in its name.

The Labour MP Alison McGovern told the programme: “It’s horrific, watching that [report] makes me feel sick. The day Jo was killed was one of the worst days of my life, and to think a discussion was going on makes me deeply upset.”

Leave.EU also secretly funded Labour Leave, the programme claimed, citing emails that suggested three staff members and office costs were paid by Banks.

Labour Leave said it was an independent organisation and was not controlled or directed by Banks or Leave.EU.

In a statement it said the “shameful” press release had nothing to do with the group, and that they had condemned it as soon as they learned it had been distributed in its name.

It said the office space was declared as a donation in kind in its final accounts, and that “this should have been declared in the running accounts during the campaign as well.” It added: “This was an administrative error, and it is incorrect to say this was not declared at all. It was.”

Channel 4 News also said Leave.EU provided staff and £67,000 of funding for a “battle bus” for Nigel Farage, then the leader of Ukip. However, Ukip declared the bus in its own spending return, and no joint spending between the two groups was ever reported.

Leave.EU hired a private jet to fly Farage to a Ukip event in Gateshead but failed to declare the spending, the programme said. Ukip told the programme both instances of spending were a matter for Farage.

Channel 4 News said Banks said on Friday night that he needed more time to respond to its questions because he was skiing in Italy. Banks tweeted that the programme was “smearing everyone” but he did not address the specific allegations.