Subglacial water flow drives the excavation of a variety of bedrock channels including tunnel valleys and inner gorges. Subglacial floods of various magnitudes – events occurring once per year or less frequently with discharges larger than a few hundred cubic metres per second – are often invoked to explain the erosive power of subglacial water flow. In this study we examine whether subglacial floods are necessary to carve bedrock channels, or if more frequent melt season events (e.g. daily production of meltwater) can explain the formation of substantial bedrock channels over a glacial cycle. We use a one‐dimensional numerical model of bedrock erosion by subglacial meltwater, where water flows through interacting distributed and channelized drainage systems. The shear stresses produced drive bedrock erosion by bed‐ and suspended‐load abrasion. We show that seasonal meltwater discharge can incise an incipient bedrock channel a few tens of centimetres deep and several metres wide, assuming abrasion is the only mechanism of erosion, a particle size of D=256 mm and a prescribed sediment supply per unit width. Using the same sediment characteristics, flood flows yield wider but significantly shallower bedrock channels than seasonal meltwater flows. Furthermore, the smaller the shear stresses produced by a flood, the deeper the bedrock channel. Shear stresses produced by seasonal meltwater are sufficient to readily transport boulders as bedload. Larger flows produce greater shear stresses and the sediment is carried in suspension, which produces fewer contacts with the bed and less erosion. We demonstrate that seasonal meltwater discharge can excavate bedrock volumes commensurate with channels several tens of metres to a few hundred metres wide and several tens of metres deep over several thousand years. Such simulated channels are commensurate with published observations of tunnel valleys and inner gorges. Copyright © 2018 John Wiley & Sons, Ltd. Subglacial flood events are overwhelmingly invoked to explain the erosion produced by subglacial water flow and the excavation of bedrock channels such as tunnel valleys and inner gorges. We use a numerical model to show that subglacial floods can inhibit bedrock channel excavation, because flood flows produce shear stresses that move the sediment away from the bed and into suspension. We show that inner gorges and tunnel valleys can be excavated over a glacial cycle by seasonal meltwater discharge