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Headington provides a wide range of of shops and services, all within walking distance of the John Radcliffe Hospital, the Churchill Hospital and the Nuffield Orthopaedic Centre.The details of these and where to find them can be found at this website:
There are a number of shopping areas within relatively close promixity (1 to 3 miles) of the Horton General Hospital. For more details, see:
Oxford City Centre has a wide selection of shops that cover all of your needs and beyond. There is anything from the usual supermarket to a specific nationality specialist shop and all sorts of niche stores that will supply anything from retro sweets to the suit for your wedding. You can find out more about the range of shops and attractions at the websites below:
Further afield, there are some great shopping outlets that are reachable via buses that go from Gloucester Green bus station in Oxford. These are just a few in the surrounding area that may be of interest: