The CoE has released a letter, signed by 84 bishops, which was sent to Prime Minister David Cameron in September, urging him to make a "meaningful and substantial response to the scale of human suffering we see daily".
Amid mounting public pressure to strengthen Britain's response to the migrant crisis on Europe's borders, the Government pledged to take in 20,000 Syrian refugees over the next five years.
The bishops write in the letter: "We believe such is this country's great tradition of sanctuary and generosity of spirit that we could feasibly resettle at least 10,000 people a year for the next two years, rising to a minimum of 50,000 in total over the five-year period you foresaw in your announcement.
"Such a number would bring us into line with comparable commitments made by other countries. It would be a meaningful and substantial response to the scale of human suffering we see daily."
The bishops also pledge to encourage their churches to provide housing and foster care to refugees as well as to support the Government in its efforts.
They also called for the creation of a National Welcome and Resettlement Board, to try to mirror the successful work carried out to help cope with past refugee crises in the 1950s and 1970s. This has been introduced since the letter was written.
It counts the Rt Rev Paul Butler, Bishop of Durham, as its co-chairman but he says it is "disheartening that we have not received any substantive reply" from Mr Cameron.
Speaking on behalf of the bishops, he said: "The Archbishop of York recently said that the current situation has rightly been described as a refugee crisis, but it is also a time of opportunity for us as a country and for our wider continent. The opportunity before us is to rise above narrow self-interest, however defined, and to embrace the highest parts of our humanity.
"We recognise that both the Prime Minister and his Government responded to calls from the country for there to be a programme of resettlement and we are grateful to him for responding to those calls.
"However there is a real urgency to this issue with those increasingly being forced from their land as their homes are literally bombed into the ground. As the fighting intensifies, as the sheer scale of human misery becomes greater, the Government's response seems increasingly inadequate to meet the scale and severity of the problem.
"It is disheartening that we have not received any substantive reply despite an assurance from the Prime Minister that one would be received. There is an urgent and compelling moral duty to act which we as bishops are offering to facilitate alongside others from across civil society."
The Bishop of Europe Robert Innes told Premier he was "disappointed" the Prime Minister did not reply to the letter: "We wrote a pretty friendly and supportive letter to the Prime Minister but we were disappointed that we didn't get a response.
"That may not be down to the government itself as down to the Home Office officials who really didn't take any action as a result of the letter we wrote.
"We'll get a response from the government, publically by the media, as a result of having brought this letter to the media's attention."
He agreed that it was disappointed the Church had to go public with its concerns in order to get a reply.
He said he didn't know if there were conversations to try and get a response before the Church took the letter public.
Alison Gelder, the Chief Executive of Housing Justice, said: "I deeply regret that the Government seem to have rebuffed this offer of help and moral leadership from the Bishops.
"The Bishops serve communities up and down the UK and see the resource locally and the call of many to welcome more than the 20,000 refugees this Government is offering.
"Housing Justice continues to receive offers of spare rooms, buildings and other accommodation (eg retreat houses and Christian conference centres) from across the churches in the longer term.
"This is welcome, but it is, though, vital that we carry on responding to the needs of homeless asylum seekers who are already here and need help now!
"I add my voice to many today seeing the Bishops letter and call on the Prime Minister to respond in the full to the Bishops to see a short, medium and long term solution, which includes building more homes to the current crisis."
A Downing Street spokesman said: "We have announced that the UK will resettle an additional 20,000 Syrian refugees over the course of this parliament.
"It is absolutely right that Britain should fulfil its moral responsibility to help the refugees, just as we have done so proudly throughout our history. But in doing so, we must use our head and our heart by pursuing a comprehensive approach that tackles the causes of the problem as well as the consequences.
"The UK is the second largest donor in the world after America, helping refugees in Syria, Lebanon, Jordan and Turkey. Our total contribution to the Syrian crisis is more than £1.12 billion."
Speaking to Premier the Bishop of Buckingham defend the decision to publish the letter.
The Bishop of Europe Robert Innes speaking to Premier's Antony Bushfield: