Microscopic sessile suspension feeders live attached to surfaces and, by consuming bacteria-sized prey and by being consumed, they form an important part of aquatic ecosystems. Their environmental impact is mediated by their feeding rate, which depends on a self-generated feeding current. The feeding rate has been hypothesized to be limited by recirculating eddies that cause the organisms to feed from water that is depleted of food particles. However, those results considered organisms in still water, while ambient flow is often present in their natural habitats. We show, using a point-force model, that even very slow external flow is sufficient to disrupt the eddies around perpendicular suspension feeders, providing a constant supply of food-rich water. However, the feeding rate decreases in external flow at a range of non-perpendicular orientations due to the formation of recirculation structures not seen in still water. We quantify the feeding flow and observe such recirculation experimentally for the common suspension feeder Vorticella convallaria in external flows typical of streams and rivers.