Nancy Pelosi, the House speaker of the US Congress, has likened the 6 January insurrection fomented by Donald Trump to 9/11, saying one had been an assault on US democracy from within and the other from the outside.

She also claimed the Republicans had been hijacked by a cult that believed neither in science or government, making it hard for the US to be governed.

Her remarks, made at a Chatham House seminar in London on Friday, arguably breach the semi-honoured rule for domestic political disputes to end at America’s water’s edge.

Pelosi a strong defender of the Northern Ireland Good Friday agreement, repeated her warning of two years ago that anything that imperilled the agreement could mean the US Congress would not ratify a free trade deal with the UK.

She was speaking at Chatham House the day after meeting Boris Johnson in Downing Street.

She said the prime minister had given her some reading material and that she would cross-examine him on the details when they met again in Washington next week.

Johnson is due to travel to the US with Liz Truss, the new UK foreign secretary, prior to the UN general assembly.

“This is not said as any threat,” Pelosi insisted. “It is a prediction. If there is destruction of the Good Friday accords we’re very unlikely to have a UK-US bilateral [trade deal].”

The bulk of her remarks were concerned with the collapse of bipartisanship within the US, and the implications for its relationships as an ally with other countries.

The 6 January demonstration, she said, was an insurrection incited by Trump, and added that it “was an assault on Congress, constitution and our democracy. How we deal with it is really the measure of the strength of our democracy.”

She also challenged Republican senators for rejecting the congressional commission into the Capitol attack, asking: “Why do they reject finding the truth of what happened in January? Is it because they had some sympathy for the cause?”

She compared the 6 January protest with 9/11, saying while the attack in 2001 had been an “assault from outside”, the Capitol attack was an “assault from within”.

“Horrible in both cases. What had happened to our democracy on 6 January was horrible,” she said.

Although Trump did not create the problems on 6 January, she continued, “he galvanised them” with the help of social media, especially Facebook. She ironically thanked Facebook for hosting 2 million followers of the conspiracy theory QAnon on its site and said social media was a blessing, but a double-edged sword.

The roots of American populism lay in fears of globalisation, automation and immigration, and was expressed through Islamophobia, antisemitism and ideas of white supremacy, she said.

She added: “I would say to my Republican friends – and I do have some – take back your party, the Republican party. The Grand Old Party has made tremendous contributions to our country founded by Lincoln. Don’t let your party be hijacked by a cult – essentially, that is what is happening.

“This is not conservative. This is radical rightwing, off the spectrum, anti-governance and if you are anti-governance it is very difficult to govern.

“If you are in denial about climate change, if you don’t believe the science and data and won’t respond to the data, that is a problem.”

She admitted the Democrats “have a big fight on our hands whether it is in the states or nationally”. She also admitted some of the alienation was caused by inequality.

“In America, capitalism is our system, it is our economic system, but it has not served our economy as well as it should. So what we want to do is not depart from that, but to improve it.

“You cannot have a system where the success of some springs from the exploitation of the workers and springs from the exploitation of the environment and the rest, and we have to correct that.”