Theresa May has been urged to meet the Government's pledge to resettle 20,000 Syrian refugees two years early in 2018 and then offer more help to those fleeing the war.
Labour's refugee taskforce chairwoman Yvette Cooper said the Prime Minister should use next week's United Nations General Assembly summit to demonstrate British leadership on tackling the refugee crisis.
She should seek to gain support from international leaders in creating safe routes for those fleeing war and persecution and build on the UK's own commitments, Cooper said.
A first step would be to meet the pledge to resettle 20,000 Syrian refugees early because places for all of them have now been secured from local authorities.
The former cabinet minister also urged the PM to resettle 500 lone child refugees before Christmas and to ensure that no child is left alone in Calais's "Jungle" camp during the festive season.
Cooper said it was "shameful" that the Government has not resettled a single unaccompanied child refugee currently in Italy, France or Greece despite committing to do so when agreeing to the so-called "Dubs amendment" in May.
"The Prime Minister must show leadership on the refugee crisis," the Labour MP said.
"She must go to this summit to galvanise international support for refugees and show that Britain can and will meet our commitments.
"Right now the decisions Parliament and our country have taken are being mired in red tape and Government foot-dragging.
"Yet all the while lives are at risk. Britain has always done its bit to help those fleeing persecution - we have to live up to those values again now."
"It is shameful that we still haven't welcomed any lone child refugees under the Dubs amendment," she continued.
"And it is appalling that so many children and teenagers with family in Britain are still stuck in miserable and dangerous conditions in the Calais camp because of bureaucratic delays. Surely it is not beyond the wit of two great nations, Britain and France, to end the scandal of Calais."
Cooper also called on the Government to ensure international pledges made at the London Supporting Syria conference are met by Christmas, speed up family reunion for lone children, and introduce child protection measures and "proper sanctuary" for child refugees in Calais.