Policymakers often suggest that expansion of care in community settings may ease increasing pressures on hospital services. Substitution may lower overall health system costs, but complementarity due to previously unidentified needs might raise them. We used new national data on community and primary medical care services in England to undertake system-level analyses of whether activity in the community acts as a complement or a substitute for activity provided in hospitals. We used two-way fixed effects regression to relate monthly counts of community care and primary medical care contacts to emergency department attendances, outpatient visits and admissions for 242 hospitals between November 2017 and September 2019. We then used national unit costs to estimate the effects of increasing community activity on overall system expenditure. The findings show community care contacts to be weak substitutes with all types of hospital activity and primary care contacts are weak substitutes for emergency hospital attendances and admissions. Our estimates ranged from 28 [95% CI 21, 45] to 517 [95% CI 291, 7265] community care contacts and from 34 [95% CI 17, 1283] to 1655 [95% CI - 1995, 70,145] GP appointments to reduce one hospital service visit. Primary care and planned hospital services are complements. Increases in community services and primary care activity are both associated with increased overall system expenditure of £34 [95% CI £156, £54] per visit for community care and £41 [95% CI £78, £74] per appointment in general practice. Expansion of community-based services may not generate reductions in hospital activity and expenditure.