Automated Vehicles (AVs) rely on up-to-date map information to inform trajectory prediction and planning modules, but these maps are expensive to obtain and update as they are usually annotated by humans. We propose SAM-Maps, a method for automatically generating road maps from aerial images of urban areas that takes advantage of the power of foundation models, requiring no human annotation or additional training to map unseen areas. This method extracts a coarse road graph from the images and then estimates the geometry of the roads from this graph. We evaluate our model on the challenging road layouts of the recent View-of-Delft Prediction dataset by comparing the maps generated using our model to the human-annotated maps, achieving an IoU of 33.3% with our automatic method and an IoU of 56.1% with some human corrections in our method. We also evaluate a trajectory prediction model on our maps to test whether they are sufficiently accurate for downstream tasks. The performance of this model using the map from our automatic method is 37.9% better on the minADE6 metric than not using map data as input. To the best of our knowledge, this is the first method that extracts both the drivable area and road connections of European urban areas from aerial images. The code will be publicly released for research purposes.