The soil and vegetation of urban greenspace can potentially contribute to ambitious climate action plans declared by city institutions and councils. To assess how urban greenspace could make a contribution to institutional carbon management, we measured soil carbon at 42 sampling locations across three land‐covers and vegetation carbon of 490 trees (67 species), over the city campus of Newcastle University. Soil carbon varied with pH and land‐cover classes (lawned with some free‐standing trees, woodland park, sports fields), and tree cover significantly enhanced soil carbon storage. Soil carbon storage from 0 to 30 cm depth averaged 18.85 kg·m−2, more than double the tree carbon storage (average 7.66 kg·m−2) estimated using biomass empirical equations. According to our scenarios, even if all currently available urban greenspace were converted to woodland, this would offset only 1% of current annual greenhouse gas emissions of Newcastle University or, if implemented more widely, of Newcastle city overall. While urban woodland brings benefits beyond carbon storage, the limit to what can be achieved within cities emphasizes the need for urban–rural partnerships. In exchange for helping cities with carbon abatement, their surrounding rural regions could benefit from carbon offsetting payments to improve their infrastructure provision. Overall, a carbon‐friendly and nature‐based land management strategy should be developed with full consideration of collaborative partnerships between urban and surrounding rural areas, particularly placing a high value on soil and tree carbon.