Flow control apparatus, for placement in a downhole location in the tubing string of a well. The apparatus comprises a valve element and a lock element. Application and removal of annulus pressure (on the annulus between the tubing and the casing) permits the apparatus to be cycled between a sensitive-to-flow mode, in which it opens to permit fluids to be injected down the tubing into a subsurface formation, but closes to prevent fluid backflow from the subsurface formation into the tubing; and an insensitive-to-flow mode, in which the apparatus is open to permit unimpeded fluid flow in either direction.