In footage that was widely shared on social media, she called for listeners to “get the names” of people delivering Covid vaccines and email them to her.
“With a group of lawyers we are collating all that,” she continued. “At the Nuremberg trials the doctors and nurses stood trial and they hung. If you’re a doctor or a nurse, now is the time to get off that bus. Get off it and stand with us the people – all around the world they are rising.”
Ms Shemirani, who has frequently compared Britain’s response to coronavirus to Nazi Germany, led Saturday’s protests and introduced other speakers including conspiracy theorists David Icke and Piers Corbyn, and far-right activist Katie Hopkins.
Following uproar over her comments, she defended what she called a “very informative speech” and denied inciting murder.
In a video posted on the encrypted messaging app Telegram on Sunday, Ms Shemirani said: “It’s being stated that I called for the nurses and doctors of the NHS to hang, which is simply not true. It’s a case of Chinese whispers … I gave a very informative speech.”
Her son, Sebastian Shemirani, called for her to be prosecuted and said she was “beyond help” over her views.
“She should be prosecuted under existing laws or if there aren’t existing laws in place that say that what she’s doing is illegal, then we should be having a national conversation about what laws we should be bringing in,” he told BBC Radio 4’s Today programme on Monday.
“It’s only a matter of time before somebody acts on the bad advice that she’s giving the country.”
Several politicians have called for a police investigation over the Nuremberg comments.
Sir Keir Starmer, the Labour leader and former director of public prosecutions, told LBC radio Ms Shemirani’s statements were “shocking” and added: “I do hope it’s going to be investigated and dealt with appropriately.”
Sadiq Khan, the mayor of London, said he raised the “appalling” speech with the Metropolitan Police and called NHS staff the “heroes of the pandemic”.
A spokesperson for Scotland Yard said: “We are aware of video circulating online showing a speech that occurred during a rally in Trafalgar Square.
“Officers are carrying out enquiries to establish whether any offences have been committed. No arrests have been made.”
Ms Shemirani was struck off as a nurse earlier this year after a misconduct investigation by the Nursing and Midwifery Council.
It found that she had “abused her position of trust” and put the public at risk of harm with false claims, adding: “She is using her status as a registered nurse to portray herself as someone who has more specialist knowledge than the average member of the public, and she is using this to promote misinformation.”
A report warned that her speeches and social media posts “could have serious consequences for those who listen to her damaging and distorted messages”.
The Royal College of Nursing called Ms Shemirani’s latest comments “reprehensible” and said they could put staff at risk, while the British Medical Association called for action to protect frontline workers against “appalling abuse”.
The organisers of the “World Wide Rally for Freedom” on Saturday claimed that protests would take place in more than 180 cities across the world.
They said they were protesting against continued coronavirus restrictions, mask rules, compulsory vaccinations and vaccine passports.