Only two refugee families have been resettled under a sponsorship scheme launched six months ago.
It is claimed that dozens of groups are ready to take part but their applications have been stuck in a queue.
The Home Office said the Government's intention has always been that the scheme would start on a small scale.
Home Secretary Amber Rudd unveiled the Community Sponsorship initiative in July.
Churches, charities, faith groups and businesses can provide housing and support for those brought to Britain from Syria and other countries in the Middle East and north Africa.
Lambeth Palace was the first sponsor approved under the scheme and it was revealed at the launch last year that a family was living in a cottage in the grounds of the historic London residence of the Archbishop of Canterbury.
Campaigners pointed to figures showing that Canada has resettled more than 13,000 Syrian refugees through private sponsorship since November 2015.
The issue was raised as representatives of the Global Refugee Sponsorship Initiative arrived in the UK for talks with ministers.
Gregory Maniatis, senior migration adviser at The Open Society Foundations, said: "Sponsorship is not only an important way to help refugees fleeing war, but it also creates an outlet for communities to express their compassion and to bring people together around a meaningful cause.
"It changes the lives of natives in a positive way nearly as much as those of newcomers."
A Home Office spokesman said the Government is on track to meet a commitment to resettle 20,000 Syrian refugees by the end of this Parliament, with more than 4,400 people granted humanitarian protection so far.
The spokesman said: "Community Sponsorship - a ground-breaking development for resettlement in the UK - is part of this work and our intention has always been that this relatively new scheme would start on a small scale and be monitored closely to ensure it delivers positive outcomes for resettled families and local communities.
"We have seen considerable interest in the scheme from across the UK and are working with a number of groups as they develop their plans.
"Supporting a vulnerable resettled family is a significant responsibility and it is only right that we carefully assess every sponsoring organisation."
The Home Office said the approval process ensures each prospective sponsor has sufficient resources and a credible plan for supporting a resettled family, and does not present a risk to the family.