At a Home Affairs Select Committee on Wednesday, the Home Secretary told Tim Loughton there are "safe and legal routes" but did not go into detail, despite being pressed.
The East Worthing and Shoreham MP gave Ms Braverman a “role play” scenario of a 16-year-old from an unspecified African country looking to come to Britain.
He said that while migrants escaping wars in Syria, Afghanistan and Ukraine have a path, he wanted to know how others could be given asylum.
Ms Braverman said: "If you're able to get to the UK you're able to put in an application for asylum. If you put in an application for asylum upon arrival that would be the process you would enter.”
But Mr Loughton said he wanted to know how a teenage migrant crossing the Channel and arriving in Britain by illegal means could seek asylum. Ms Braverman did not answer but was helped out by Home Office permanent secretary Matthew Rycroft.
He said the teen could talk to the UN's refugee agency "depending which country you're from" to get leave to enter the UK to put in an asylum, but admitted this may not be possible from all countries.
The Home Secretary was facing questions over the Manston migrant processing centre, which has gone from being overcrowded to having no claimants currently there.
She was unable to answer right away how many judicial reviews have been launched over the treatment of migrants at the site although the committee's chairman Dame Diana Johnson said she had heard four have been launched.
Ms Braverman later said none have in fact been launched but five pre-action protocol letters have been received.
In response to a question of general policy by Tory MP Lee Anderson, Ms Braverman said: "We have failed to control our borders, yes. That's why the Prime Minister and myself are absolutely determined to fix this problem."
And responding to a question as to whether migrants could be put on a flight to Rwanda against their will, Ms Braverman said the “courts” would decide the verdict.
Hackney MP Diane Abbott asked if Rwanda was a safe place for migrants to be sent, to which Ms Braverman said it was - having passed government assessments.