Listings >> Shopping >>Supermarkets Putney Convenience Store Putney off licence. Putney Convenience Store is a handy shop located on Putney High Street selling all of your basic needs. Customers are able to purchase groceries, drinks, stationary, newspapers, magazines, phone top-ups and much more. Putney High Street 69A London SW15 1SR England GB Get directions Shopping_ico Created with Sketch. Shopping Supermarkets Monday-Thursday: 6.30-23.00 Friday and Saturday: 6.30-00.00 Sunday: 6.30-23.00 020 8785 0950 Photo gallery All photos (1) Shopping_ico Created with Sketch.