She said it was her personal view and acknowledged Government policy was to work within the boundaries of the convention, which is interpreted by the European Court of Human Rights.
But it is another sign of indiscipline within Liz Truss’ administration at the Tory conference in Birmingham.
A senior Government source told the PA news agency: “As Suella acknowledged, her personal views are contrary to Government policy and if she wishes to make those views known within Government she should do so in a more appropriate setting.”
Ms Braverman campaigned on the issue when she stood for the Tory leadership in the contest won by Ms Truss.
She told a Spectator event at the Tory conference in Birmingham: “I was pretty blunt about this issue in my leadership campaign.
“My position personally is that ultimately we do need to leave the European Convention on Human Rights.
“That is not government policy, I should say, government policy is to do everything we can within the convention, within the boundaries of the convention.
“But if that doesn’t work, then we will have to consider all options.”
She added: “I don’t think we need to be subject to an institution born out of the post-war era which is a bit analogue in the way that it operates, which has centralised power, which is distant and which is politicised, which is pursuing an agenda which is at odds with our politics and our values.
“I don’t think that’s the direction that the world is going in, that’s not the direction that people called for with Brexit.”
An intervention by the European court contributed to the grounding of the first flight under the Government’s policy of sending asylum seekers to Rwanda.
In her main conference speech, Ms Braverman said migrants crossing the Channel will face a ban from claiming asylum in Britain.
The new laws – which go further than the Nationality and Borders Act which came into force in June – will impose a blanket ban on anyone deemed entering the UK illegally from seeking refuge.
The announcement marks the latest attempt by the Government to curb the growing numbers of Channel crossings after its flagship policy to send migrants on a one-way trip to Rwanda stalled amid the legal challenges.
So far this year more than 33,500 people have arrived in the UK after making the journey from France.
Ms Braverman told the conference in Birmingham the law “simply isn’t working” and legislation was being “abused” by people smugglers, people making “multiple, meritless and last-minute claims” and – taking aim at lawyers – by “specialist small boat-chasing law firms”, adding: “This cannot continue.”
“I will look to bring forward legislation to make it clear that the only route to the United Kingdom is through a safe and legal route … So if you deliberately enter the United Kingdom illegally from a safe country, you should be swiftly returned to your home country or relocated to Rwanda. That is where your asylum claim will be considered.”
Campaigners condemned the plan as further “attacks” on “genuine refugees” and branded them a “blatant breach” of Britain’s international obligations under the Refugee Convention.
Clare Mosley, founder of refugee charity Care4Calais, said the proposal was “barbaric and unnecessary” while claiming the Government’s rhetoric on Channel crossings was “simply false”.
Enver Solomon, chief executive of the Refugee Council, branded the proposals “deeply worrying and out of step with the majority of the public who support giving refugees protection”.
Zoe Abrams, executive director at the British Red Cross, said: “We need more safe routes for people at risk. The vast majority of people that make it to our shores go on to have their asylum claim approved.”
Setting out her intention to ensure UK immigration policy is not “derailed” by modern slavery laws, the Human Rights Act or the European court, Ms Braverman also said she would “work closely with the French to get more out of our partnership”.
Ms Braverman insisted it was not “racist” to “want to control our borders”, or “bigoted to say that we have too many asylum seekers who are abusing the system”.
“It’s not xenophobic to say that mass and rapid migration places pressure on housing, public services and community relations. I reject the Left’s argument that it is hypocritical for someone from an ethnic minority to tell these truths,” she added.
Channel crossings continued on Tuesday after the Ministry of Defence (MoD) recorded 541 arrivals in nine boats on Monday. In September, 7,961 made the crossing to the UK.
Earlier on Tuesday, Ms Braverman told a conference fringe event she would “love to be here claiming victory, I would love to be having a front page of the Telegraph with a plane taking off to Rwanda, that’s my dream, that’s my obsession”.