The Home Secretary confessed to more breaches on Monday having sent six emails in as many weeks, but insisted none of them were “top secret”.
Monday saw Ms Braverman label people coming to Britain an “invasion”, and say her critics opposed her because she wanted to end illegal migration.
It comes amid questions over her handling of the Manston processing centre in Kent, where outbreaks of MRSA and diptheria have been reported.
The site is only designed to hold 1,000 people, who are meant to stay for just 24 hours, but there are currently around 4,000 migrants there.
Making a statement in the Commons, she said: “I am utterly serious about ending the scourge of illegal migration and I am determined to do whatever it takes to break the criminal gangs and fix our hopelessly lax asylum system.
“That is why I am in government, and that is why there are some people who would prefer to be rid of me.”
Ms Braverman was heckled by Labour MPs, before adding: “Let them try. I know that I speak for the decent, law-abiding, patriotic majority of British people from every background that wants safe and secure borders.
“Labour is running scared that this party might just deliver them.”
Ms Braverman also told MPs she is serious about “stopping the invasion” on the southern coast of England, saying people should “stop pretending that they are all refugees in distress.”
She continued: “Let’s be clear about what is really going on here: the British people deserve to know which party is serious about stopping the invasion on our southern coast and which party is not.
“Some 40,000 people have arrived on the south coast this year alone. Many of them facilitated by criminal gangs, some of them actual members of criminal gangs.
“So let’s stop pretending that they are all refugees in distress. The whole country knows that is not true. It’s only the honourable members opposite who pretend otherwise.
“We need to be straight with the public. The system is broken. Illegal migration is out of control and too many people are interested in playing political parlour games, covering up the truth than solving the problem.”
Her responses prompted laughter from Labour MPs, who claimed it was her party who were responsible.
There was also criticism from Tories, with Sir Roger Gale blaming ms Braverman for the crisis at Marston.
The North Thanet MP said: “That facility operated absolutely magnificently and very efficiently indeed until five weeks ago, when I’m afraid the Home Secretary took the policy decision not to commission further accommodation and it is that, that has led to the crisis at Manston.”
Ms Braverman insisted she “worked hard to find alternative accommodation”.
On a damaging day for the Home Secretary, she earlier admitted to more breaches of the ministerial code.
In a letter to the Commons Home Affairs Select Committee’s chairwoman Dame Diana Johnson, Ms Braverman apologised for the breach.
She said she had apologised to Rishi Sunak when she was reappointed as Home Secretary when he entered No 10 and publicly repeated that apology.
Ms Braverman explained: “In my appointment discussion with the new Prime Minister, I raised this mistake and apologised to him, and would like to do so again here.
“I also gave the Prime Minister assurances that I would not use my personal email for official business and reaffirmed my understanding of and adherence to the Ministerial Code.”
Manston: Pressure mounts of Suella Braverman amid worsening conditions and overcrowding at migrant processing centre
The Home Secretary insisted there was nothing market sensitive in the draft written ministerial statement (WMS) she sent from her private email address to Tory backbencher Sir John Hayes.
“None of the documents in question concerned national security, intelligence agency or cyber security matters, and did not pose any risk to national security. None of the documents were classified as SECRET or TOP SECRET.”
She said former prime minister Liz Truss had “specifically” asked her to engage with parliamentary colleagues to discuss the content of the planned WMS.
The draft WMS consisted of “high-level proposals for liberalising our migration rules”, including “increasing the number of low-skilled foreign workers, as well as general plans for controlling illegal migration”.
The Prime Minister’s official spokesperson claimed she had set out a “detailed account”.
He said: “She has provided a detailed account around those issues, both the individual issue of forwarding that email and a further investigation.
“I think she has set out in quite a lot of detail what has happened and the mitigations that have been taken.
“Clearly, as she makes clear, she made an error of judgment, she recognises that the approach she took was not right and it is for those reasons that she felt it was right to resign, and obviously she has apologised, both to the Prime Minister, the MP involved, and she has set out a detailed letter to the committee today.”
Yvette Cooper, Shadow Home Secretary, responding to the letter from Home Secretary, said: “This letter fails to answer all the serious questions about the Home Secretary’s irresponsible conduct and shows that neither she nor the Prime Minister recognise the gravity of these issues.
“The Home Secretary has now admitted she sent government documents to her personal phone six times in 43 days - that’s once in every week she was in the post.
“There are still significant inconsistencies in the information in this letter and her original resignation letter. There are also still no answers about alleged security breaches and leak investigations while she was Attorney General or about whether the Prime Minister ignored the Cabinet Secretary’s advice in reappointing her just 6 days after she was forced to resign.
“It is also astonishing that as Home Secretary in charge of national security and former Attorney General she has therefore needed to seek an additional briefing on “what constitutes appropriate use of Government and personal IT.
“This therefore leaves more unanswered questions, more confusion and more chaos from the Home Secretary and the Government. It shows why Rishi Sunak was so irresponsible in reappointing her to her post.”
The SNP claimed the Home Secretary's position is now "completely untenable" following the crisis at Manston.
SNP Home Affairs spokesperson Stuart McDonald MP said: "Rishi Sunak must sack Suella Braverman and take personal responsibility for fixing the appalling crisis at Manston, which has happened on the Tory government's watch.
"The Home Secretary's position is now completely untenable. She should never have been reappointed following her breach of the ministerial code, and now we find she's guilty of a staggering dereliction of duty and error of judgement over asylum processing.
"Ms Braverman must come out of hiding, admit responsibility for the catastrophic failure to do the very basics of her job and pack her bags. And the Prime Minister must answer for the dodgy backroom deal that he made with Ms Braverman to shore up his own position."