Just been re-digging the bit where the potatoes were to check that we got them all out of the ground.
It is best not to leave any in and also to remember to plant next years potatoes in a different area of the vegetable plot. that helps to reduce the risk of disease in future crops.
Crop rotation is covered in gardening books there are several ways to approach it.
Basically it is about planting different types of crop in an area than the crop you raised in that area/spot this year.
It is an idea that is simple to do and worth following through to prevent problems in the future.