MPs will take part in an emergency debate on the refugee crisis tomorrow after an application from Labour leadership candidate Yvette Cooper.
Ms Cooper said David Cameron's plans to accept 20,000 Syrian refugees over the next four and a half years does not go far enough and had her call for an emergency debate backed by enough Labour MPs to force it on to tomorrow's business.
The shadow home secretary insisted Britain must also help refugees who have made it to Europe as well as the Prime Minister's current proposal to take more from camps surrounding Syria.
Ms Cooper said "20,000 over five years could mean 4,000 a year".
She went on: "The Kindertransport took 10,000 children in the space of nine months.
"I would urge the Prime Minister to reconsider and to look at what more we are able to do with councils, with communities across the country who have come forward asking to help and do more.
"The Prime Minister has rightly changed his mind already in response to the public concern - I ask him to do so again and for the opportunity for this House to persuade him to do so given the urgent need of those for help and given the importance of this debate."
"Secondly, I would ask the Prime Minister to consider again helping those who are in Europe and who need help at the moment.
"He has said he does not want to encourage people to travel - I would say to him they are travelling already, they are not waiting for a response from the British Government."
Ms Cooper spoke after the Prime Minister set out plans to take in up to 20,000 Syrians by May 2020.
Mr Cameron said Britain will use the established UNHCR process to identify those most in need and indicated that Christians and Yazidis who face persecution in camps could be included.
Those who arrive will be granted five-year humanitarian protection visas and councils and devolved administrations will be helped to support them as the Government retools its aid budget.
The PM said: "We have already provided sanctuary to more than 5,000 Syrians in Britain and have introduced a specific resettlement scheme, alongside those we already have, to help those Syrian refugees particularly at risk.
"But given the scale of the crisis and the suffering of the Syrian people it is right that we should do much more.
"We are proposing that Britain should resettle up to 20,000 Syrian refugees over the rest of this parliament.
"In doing so we will continue to show the world that this is a country of extraordinary compassion, always standing up for our values and helping those in need.
"Britain will play its part alongside our other European partners but because we are not part of the EU's borderless Schengen agreement or its relocation initiative, Britain is able to decide its own approach."
Angus Robertson, the SNP's leader in Westminster, welcomed the Government's decision to accept more refugees but said it was a "shame" it is being spread over the next five years.
Home Affairs Committee chairman Keith Vaz called for Mr Cameron to consider accepting some refugees who are already in Calais and elsewhere in Europe who have ties to the UK but the PM dismissed his suggestion.
The Labour MP said: "I agree with you that direct recruitment should be from the camps.
"However there will be exceptional cases of people who have arrived in Europe, some of whom I have met in Calais, who have ties with the United Kingdom who may need to be processed who have already arrived in mainland Europe."
Mr Cameron replied: "Anything that suggests that Calais is going to become a processing centre for people to come to the United Kingdom would simply make the situation there worse.
"We need to explain to people, if you come to Calais, if you try to get through the tunnel, that is not the way you are going to get to the United Kingdom. That's what all the security and the defence is about and we should keep it up."