The only location for general supplies is the Cotswold Service station in Old Sodbury.
Here you can find general supplies for your walk (snacks/food/water) - Interestingly, it has some random assortment of American-based snacks also! If for any reason this store has closed down, please let us know.
This is a petrol station so opening hours may vary year on year and can be seasonal. Be aware that on UK bank holidays and school holidays standard opening hours may differ also.