The pro-EU MP for Broxtowe was interrupted while doing live interviews on Monday on College Green, across the road from the Palace of Westminster in the heart of London.
With the home of British politics clear in the background, she was forced to stop talking during a BBC discussion while people off-camera could be heard shouting “Soubry is a Nazi”.
She told interviewer Simon McCoy: “I do object to being called a Nazi, actually.
“I just think this is astonishing, this is what has happened to our country.
“But let’s try and move on and be positive about things.”
Protestors also chanted slogans including “Liar, liar” throughout a live interview by Ms Soubry on Sky News.
Speaking up to be heard over the chants, Ms Soubry told interviewer Kay Burley: “I don’t have a problem with people demonstrating and making their views heard. I have a real problem with people who call me a traitor or ‘Soubry, you Nazi’. That is a criminal offence and I’m a criminal barrister.
“I’m also a lass from Worksop, so I don’t get scared by these people or intimidated. I was a reporter during the miners’ strike, so I don’t feel physically intimidated. My difficulty is I want to respond and you mustn’t, so I’m really behaving myself.”
Ms Soubry said the incident was “seriously worrying”, adding: “I’m afraid the truth is that Brexit has unleashed these people. This is Britain now. This is not the country I know and love and these people do not represent our country and they need sorting out.”
She added: “I’m told that we should get used to it, but we shouldn’t have to. Apparently it’s democracy in action and the CPS (Crown Prosecution Service) believe that no offences are being committed.”
The protesters were criticised by high-profile Brexit supporters including presenter Piers Morgan and Douglas Carswell, the former Conservative and Ukip MP.
Writing on Twitter, Mr Carswell said: “Small crowd shouting oafish chants at TV crew outside Parliament.
“I’m not a great fan of the mainstream broadcasters, but such boorishness is out of line.
“Do they realise how much damage they do?”
Broadcasters carrying out live interviews outside Parliament have found themselves having to deal with noisy attempts at interruption from protesters from across the Brexit divide in the run-up to March’s planned withdrawal.
They include pro and anti-Brexit supporters who have shouted and waved flags during broadcasts.
Theresa May’s official spokesman said he had not discussed the incident involving Ms Soubry with the PM, but added: “The Prime Minister has been very clear that nobody involved in the political process should be subjected to abuse or harassment.”
Labour MP Stephen Doughty raised the issue in the Commons during a Brexit question session and called on Speaker John Bercow to intervene.
The Cardiff South and Penarth MP said: “Can I urge you to use your offices with the Metropolitan Police at the highest levels to ensure that proper action is taken on this?”
Brexit Secretary Steve Barclay responded: “Obviously I won’t have seen the incidents outside but anyone who stands at this despatch box is always mindful of the plaque of Jo Cox, which I know is so dear to many, particularly on the benches opposite, but across the House.
“I think all of us would unite on that wherever people are on the Brexit debate … all of us in this House should be able to air their views with respect.”