Glasgow's Archbishop Philip Tartaglia was speaking after the first meeting of the Scottish Leaders' Group on Welfare Reform.
Members of the group heard what impact the UK government's welfare changes had on people and the charities that help them.
Since the election in 2010 the coalition government has placed a cap on the amount of benefits people can receive and introduced the Spare Room Subsidy that means people on housing benefit with more bedrooms than they needed had their benefits cut.
The Archbishop of Glasgow said: "We heard first-hand accounts from people who have been failed by the system through no fault of their own.
"The mechanisms for claiming benefits are not fit for purpose. Money is there, set aside from taxation, but people face an impenetrable bureaucratic jungle to try to access payments.
"Changes have been made without sufficient training and the system is being depersonalised. The result is that people are being left in desperate situations without support.
"I would want to say to those in power in London, because it is there that these decisions still are made, that they need to look closely at the reality on the ground in places like Glasgow and see the failings in the structures. And I would ask them to do all they can to put things right."
The government says it is aiming to make the benefit system fairer and more affordable, reduce poverty, worklessness and welfare dependency.