These pictures show a typical stirrup pump found in a garage after many years. This one is made by the Sutty Company and is of a very straight forward construction.
Pressing down on the handle causes a piston to descend the barrel of the pump and expel air into the tyre through the hose. Non return valves are present in the hose in most cases. Many of the famous manufacturers made these pumps, including Kismet and Hatherley & Davidson. In some cases these had beautiful brass barrels with polished wooden handles. Although I'm mainly interested in foot pumps, I do offer a repair service for these stirrup pumps.