Just 350 lone child refugees will be welcomed to the country from Europe under the so-called Dubs Amendment.
Campaigners had hoped the government would allow 3,000 minors to come to the UK under the scheme, which the government was forced to accept after a rebellion in parliament.
The Home Office said in a written statement the scheme will end in March because local authorities can't cope with anymore arrivals.
Bishop of Croydon, Rt Rev Jonathan Clark, said that wasn't true. "I think her data is just wrong," he said on Premier's News Hour.
"I understand that there are a number of councils who are very willing to take more unaccompanied child refugees," he added.
The bishop was involved in welcoming a group to his area and said: "We felt that we had a good faith agreement with the government about a good way of approaching things and now that rug has been swiped out from under our feet.
"So yes, there is a sense of betrayal. Certainly great disappointment".
He added: "This appears to be a deliberate decision of will by the Government rather than being forced on them and runs against the spirit of Lord Dubs' original amendment.
"But most importantly there is a crying human need from children who will otherwise get into the hands of traffickers.
"By refusing to help those children you are in effect helping the trafficking industry."
The government says taking more unaccompanied children would encourage people to make the "perilous journey to Europe".
A Home Office spokesperson said: "We are not giving up on vulnerable children who are fleeing conflict and danger.
"Thanks to the good will of the British public and local authorities in the last year alone we have provided refuge or other forms of leave to more than 8000 children.
"We're also clear that behind these numbers are children. It's vital that we get the balance right between enabling eligible children to come to the UK as quickly as possible and ensuring local authorities have capacity to host them and provide them with the support they will need".
Home Secretary Amber Rudd told the commons that the scheme was acting as a "pull factor" for children to make "perilous journeys to Europe".
But Head of Advocacy at Christian Aid Tom Viita told Premier: "Unfortunately the evidence doesn't really suggest that's the case.
"People who are moving because of desperate, poverty, conflict or oppression often have very few choices and very few safe and legal routes to get to safety - that's what's causing the problem".
He also dismissed her claims that councils could not cope with any more people as "ridiculous".
"Actually I think the government is rather passing the buck to local authorities as a way of diverting responsibility for this".
Tom Viita speaking to Premier's Antony Bushfield:
Bishop of Croydon, Rt Rev Jonathan Clark speaking to Premier's Marcus Jones:
