I can see in this file (https://github.com/ReactTraining/react-router/blob/v0.13.3/modules/createRouter.js) that there is a refresh function but I have no idea how to call i
You don't really need react-router for this. You can just use location.reload:
react-router
location.reload();
Also that version of react-router you linked to is very old, I think it's linking to v1 when it's currently on v4.