The organisation is demanding that the Government step up its work to meet the challenges of climate change. As well as funds from Defra, it wants the Government to mark the Queen's Jubilee in 2012 with the opening of hundreds of new greenways across the country.
The call comes as CABE launches its new Sustainable Cities initiative, which provides action points and training for the people responsible for planning, designing and managing towns and cities.
It includes a website that is the result of a two-year research programme, www.sustainablecities.org.uk, led by CABE.
As part of the initiative, CABE has published Hallmarks of a Sustainable City, a report that sets out the policies needed to create well-designed, low-carbon places.
Green infrastructure and public spaces are key elements of the Sustainable Cities initiative and form a third of its six critical sustainability themes.
CABE director of campaigns and education Matt Bell said there needed to be a greater focus on climate change adaptation through green infrastructure.
He added that the next year would be critical in lobbying and said that a number of organisations, including British Waterways and green-space bodies, are already planning to exert pressure to promote the concepts.
The report highlights examples of sustainable places, including Vauban in Germany, where four out of 10 homes are without cars, and New York's new High Line linear park, which has been created on a disused railway line.
"It would be difficult to overstate the vital role green infrastructure can play in preparing towns and cities for climate change," states the report. "So government needs to promote green networks much more boldly as an integral part of infrastructure planning."