She said hundreds of people could not reach Kabul airport or the Baron Hotel – where many British nationals have been told to travel to for processing.
It comes as the US warned its citizenswith Avoid The Airport, continued chaos outside the terminal.
The Foreign Office said it was trying to get people out as fast as possible.
Ms Nandy told the foreign secretary: “My office is currently in touch with hundreds of people who cannot reach the Baron Hotel or Hamid Karzai International Airport, have been beaten at checkpoints or turned away – some with young children.”
She said many of those stranded at the airport perimeter were women or girls, asking Mr Raab to consider establishing a military policing operation with Nato allies “just outside the gate, or a processing zone insideTaliban militants have been manning checkpoints around the perimeter of the airport and blocking Afghans without travel documents from entering.
Twelve people have been killed in or around Kabul airport since Sunday, according to a Taliban official quoted by the Reuters news agency.
But even those with valid papers have struggled to get to the airport, with reports that some have been beaten by Taliban guards.