Global peatlands store more carbon than is naturally present in the atmosphere(1,2). However, many peatlands are under pressure from drainage-based agriculture, plantation development and fire, with the equivalent of around 3 per cent of all anthropogenic greenhouse gases emitted from drained peatland(3-5). Efforts to curb such emissions are intensifying through the conservation of undrained peatlands and re-wetting of drained systems(6). Here we report eddy covariance data for carbon dioxide from 16 locations and static chamber measurements for methane from 41 locations in the UK and Ireland. We combine these with published data from sites across all major peatland biomes. We find that the mean annual effective water table depth (WTDe; that is, the average depth of the aerated peat layer) overrides all other ecosystem- and management-related controls on greenhouse gas fluxes. We estimate that every 10 centimetres of reduction in WTDe could reduce the net warming impact of CO2 and CH4 emissions (100-year global warming potentials) by the equivalent of at least 3 tonnes of CO2 per hectare per year, until WTDe is less than 30 centimetres. Raising water levels further would continue to have a net cooling effect until WTDe is within 10 centimetres of the surface. Our results suggest that greenhouse gas emissions from peatlands drained for agriculture could be greatly reduced without necessarily halting their productive use. Halving WTDe in all drained agricultural peatlands, for example, could reduce emissions by the equivalent of over 1 per cent of global anthropogenic emissions.