Ms Begum, now 20, was one of three east London schoolgirls who travelled to Syria to join the so-called Islamic State group (IS) in February 2015.
She lived under so-called Islamic State (IS) rule for more than three years before she was found, nine months pregnant, in a Syrian refugee camp in February last year.
Then-home secretary Sajid Javid revoked her British citizenship on national security grounds later that month.
In February this year, the Special Immigration Appeals Commission (SIAC) found Ms Begum "cannot play any meaningful part in her appeal and that, to that extent, the appeal will not be fair and effective".
But SIAC ruled that "it does not follow that her appeal succeeds" and Ms Begum’s challenge to the Home Office’s decision to refuse to allow her to enter the UK to effectively pursue her appeal was also rejected.
The judge found that "the national security concerns about her could be addressed and managed if she returns to the United Kingdom".
Lord Justice Flaux also said: "With due respect to SIAC, it is unthinkable that, having concluded that Ms Begum could not take any meaningful part in her appeal so that it could not be fair and effective, she should have to continue with her appeal nonetheless."
He added: "It is difficult to conceive of any case where a court or tribunal has said we cannot hold a fair trial, but we are going to go on anyway."
The government said it was "bitterly disappoint" by the ruling and Mr Javid said he was "deeply concerned" by the judgment.
The Home Office immediately announced its intention to seek permission to appeal against the ruling at the UK’s highest court, an application which is due to be considered by the Court of Appeal on Friday morning.
Even if the Court of Appeal refuses permission, the Home Office could still renew its application for permission to appeal directly to the Supreme Court.
The hearing, which will be conducted remotely via Skype, is due to begin at 9.30am on Friday morning.