Christians must not be defeated by the enormity of the tasks facing them, the Archbishop of Canterbury indicated last night. Just because they cannot put everything to rights, they must not be tempted to do nothing at all.

The Most Rev Justin Welby was speaking after a new survey showed Christians, Muslims, Jews and other faiths contribute more than £3 billion a year to social action in their communities.

The enormous economic and social impact of this can be shown by contrasting the £3 billion faith contribution with the total budget of just £95.6 billion that NHS England has to deliver its mandate.

The Faith Action Audit, the most comprehensive report of its kind, was launched in Westminster last night by the Cinnamon Network. It examined the work of all kinds of faith groups in dealing with issues such as debt, addiction, homelessness and social isolation in 57 cities, towns and villages. The results were then extrapolated to give a national picture.

Archbishop Welby said the audit was a good reminder that the work of churches was "emphatically" not done by Archbishops but by local communities. "In the most extraordinary way, it springs out of the presence of God," he said.

"As Christians we believe these projects are part of letting the light shine. They witness to the reality of what faith is about." He said there was a difference between religion and faith, but usually only those within a faith understood that difference.

The recession of 2008 had revealed the problems of cities built on material wealth alone. All that was left were eternal values, and from 2008, faith groups began to spring up to fill in the gap that "opened up" as a result, he said. "The faith communities in this country have risen to the challenge of the last seven to eight years in the most extraordinary way as they have done before and will continue to do."

At the heart of it was a sense of dignity. "We should give people not just provisions, but provisions wrapped up in love, that's when human dignity is preserved. God, to show us who he was, came to live among us, [so] that when you look to Jesus you see God. And so these faith-led social action projects are part of the incarnation of what it is to show the love of God... That is why faith groups are a force for good in our society."

He admitted polls showed that young people in particular had a more negative than neutral attitude to religion.

"The faith action audit reveals something completely different. It shows the breadth, the strength, the depth of good practice."

As a "top tip", he added: "Just because you can't do everything, don't do nothing at all."

Lord Ahmad of Wimbledon, a Conservative peer and Muslim who is Under Secretary of State for Transport and the Home Office, said: "Being proud of your faith is part and parcel of what defines you. Faith is a force for good." He said local authorities recognised the value of faith groups because they have an ability to "deliver", being part of the communities they are trying to serve.

Pastor Agu Irukwu, chairman of the board of trustees of the Redeemed Christian Church of God, said the Cinnamon Network had helped faith groups achieve what they had envisioned, but had not previously had the resources to put into action. The network has helped by providing sponsorship of £2,000 per project but also by being able to pass on advice and experience of what worked and did not work.

The Cinnamon Network is appealing for sponsors to come forward with £2,000 to help get future projects off the ground.

According to the audit, time alone given by churches and other faith groups through social action projects was worth more than £200 million, which on a national level puts time given at more than £3 billion a year, supporting 48 million people.

The Cinnamon Faith Action Audit showed that if there are around 60,761 faith groups in the UK and just 47.5 per cent of them, the same percentage that completed the survey, delivered what the average group looked at by Cinnamon did, this would mean that collectively the faith sector annually delivers 220,000 social action projects, with approximately 125,000 paid staff and 1,910,500 volunteers.

Matt Bird, the founder of Cinnamon Network, who is regarded as a visionary pioneer in faith circles, said: "The audit findings were extremely revealing and leave us in no doubt about the crucial role faith groups in the UK play in delivering key social action projects in their cities or towns. As Cinnamon Network our vision is to see local churches and other faith groups more empowered and encouraged to take up their place as they serve at the heart of their community. We also want to see their work externally recognised and properly resourced as part of the overall picture of provision in any given community."