Sorry but I live in a place where supply of property, rental or otherwise, is so constrained when compared to demand that any local letting agent knows they can rent out any place within a week. You go along with whatever they say or you don't get the place. End of story.
Sorry to hear that :( In the last couple of years a number of developers flooded our town with cheap student housing units so the market has kinda been upended, much to our delight.