The All Saints Centre in Norwich is set to close on 30 June
The All Saints Centre needs £100,000 a year to keep going but has hit money difficulties because of the recession.
A plan by Bishop of Norwich Graham James to assume the lease, which could have brought a rent cut, was rejected by Norwich Historic Churches' Trust.
A spokeswoman said the trust had to protect income to maintain churches.
Felicity Hartley, vice president of the Norwich Historic Churches Trust (NHCT), said: "To put it bluntly, we have to look after our own interests.
"We have so many churches to look after we need to maximise our income."
The Bishop of Norwich is patron of the centre and was willing, as head of the diocese, to explore taking on the lease to enable the centre to continue.
The diocese said NHCT did not wish to relinquish the lease.
"It is very regrettable such excellent work has been brought to an end," a statement said.
The centre, in Westlegate, was losing £500 a week and trustees needed £22,000 to repair a damaged floor and redecorate.
Treasurer Michael Hope said the centre would shut on 30 June unless a sponsor offered £30,000 a year to keep it open.
Mr Hope said its unique character would now be lost.
Mr Hope said: "Our vision was to mix people with learning difficulties, the homeless, the lonely elderly and strangers just arriving in the city with shoppers and business people coming in for a coffee, a chat or a meal."
This had worked well during the centre's 35-year history with three-quarters of the centre's income coming from a cafe and shop. In the past year takings had fallen and Mr Hope blamed the recession.