Edith Nesbit wasn't the first to write stories featuring time travel but her Story of the Amulet (1906) may be the earliest to allow its characters to run around having adventures in time on the Whovian model. Earlier writers used time travel as a device to access one particular location- and their purpose was often didactic: Pierre Boitard had a theory of prehistory to explore, William Morris was preaching medievalism, H.G. Wells was working on his political philosophy. Nesbit, on the other hand, has her characters go here, there and everywhere for the simple fun of it. Kipling- whose Puck books have a similar feel to Nesbit's (and use the same illustrator)- keeps his modern characters from contaminating the historical record by having people from the past come to them- and tell them stories. Nesbit has no such qualms. Her children not only visit historical cruxes but meddle with them. One of her little girls inadvertently persuades Caesar to invade Britain- while another warns Ann Boleyn of her fate and betrays the gunpowder plotters.
I've used wikipedia to hunt down Nesbit's predecessors but the list may be incomplete. Well, obviously it is because Nesbit herself is missing. I'm not a wikipedia editor but perhaps someone who is could dip in and set things straight.