In the aftermath of the deadly attack on the US Capitol last year, the rightwing Fox News host Sean Hannity pleaded with a top aide to Donald Trump that there should be “no more stolen election talk” and “no more crazy people” should be admitted to the president’s orbit.

Kayleigh McEnany, the White House press secretary, agreed – but to little effect.

More than a year after the riot, around which seven people died as Trump supporters sought to stop certification of electoral college results, Trump continues to lie that the 2020 election was stolen by Joe Biden.

He also continues to keep company with far-right conspiracy theorists including Mike Lindell, the MyPillow founder who in a lawsuit this week was accused of being “crazy like a fox”.

Hannity has also long been close to Trump, as an informal adviser and sometime rally guest. Though he has been revealed to have been shaken by the attack on the Capitol, he has spent the year since the riot supporting Trump’s version of events.

The House committee investigating January 6 has asked for Hannity’s cooperation, a request a lawyer for the host said raises “first amendment concerns regarding freedom of the press”.

Hannity has previously said he does not claim to be a journalist.

Excerpts of his messages to McEnany on 7 January 2021 were included in a letter from the January 6 committee to Ivanka Trump, the former president’s daughter and adviser whom the panel also wishes to question.

“First,” the letter said, “on 7 January, Mr Hannity texted Ms McEnany, laying out a five-point approach for conversations with President Trump. Items one and two of that plan read as follows:

“1 – No more stolen election talk.

“2 – Yes, impeachment and 25th amendment are real, and many people will quit… ”

McEnany, the letter said, responded: “Love that. Thank you. That is the playbook. I will help reinforce… ”

If McEnany did follow Hannity’s playbook, it did not produce a touchdown or even a reasonable punt.

It has been widely reported that invoking the 25th amendment, which provides for the removal of a president deemed incapable of carrying out his or her duties, was seriously discussed among cabinet and White House officials.

That came to nothing but Trump was impeached a second time. He was acquitted when enough Senate Republicans stayed loyal.

On Friday, Politico published the text of a draft executive order for the seizure of voting machines and the text of a speech in which Trump would have condemned the Capitol rioters – but which he never gave.

According to the January 6 committee, Hannity also told McEnany: “Key now. No more crazy people.”

McEnany said: “Yes. 100%.”

A footnote to the letter says Katrina Pierson, another rightwing commentator, “also uses the term ‘crazies’ in her text messages, apparently to describe a number of the president’s supporters”.

Lindell continues to insist he has evidence the 2020 election was stolen, recently claiming his work could lead to the imprisonment for life of “300 and some million people”.

That prompted the Washington Post to ask: “Are you one of the one in 11 Americans Mike Lindell doesn’t want to arrest?”

In remarks at a Trump rally in Arizona last weekend, Lindell took aim at Hannity’s employer.

“When was the last time you saw anyone on Fox talk about the 2020 election?” he asked.

Fox News has continued to stoke conspiracy theories about the Capitol riot but Fox Corporation faces lawsuits regarding claims of a stolen election.

This week, Lindell joined Fox in being sued by Smartmatic, a maker of election machines.

In the suit, the company accused Lindell of knowing what he was doing – namely, trying to sell pillows – when spreading election lies.

He was, the company said, “crazy like a fox”.