Administrators were set to be appointed this week at the 52-year-old charity, which represents more than 700 civic societies.
Civic Trust representative Caroline Williams told HW the loss of Green Flag had impacted on the body's budget.
She said: "We weren't successful in our bid for the Green Flag contract or in other bids for work with government. We also work with local authorities and they have had budgetary constraints. It is a combination of different elements."
GreenSpace is part of a consortium that won the Green Flag contract. Chief executive Paul Bramhill said he was shocked to hear the Civic Trust had folded: "It's a real surprise to the whole sector but does show how difficult things are becoming. It was so established, so for it to run into this kind of trouble so quickly shows (how much) support third-sector organisations need."
The Green Flag contract was estimated to be worth £1m a year to the Civic Trust.
It was working with environmental charity Groundwork to deliver the Big Lottery Fund's £50m Community Spaces grants programme by recruiting and training facilitators to support local groups with their green space projects.
Groundwork's Community Spaces information manager Nisha Virdi said the programme was expected to continue as normal but that it was still being decided how the facilitator roles would work.
CABE Space director Sarah Gaventa added: "What (the Civic Trust) stood for is what we all stood for, so it is a real shame."