There are no large supermarkets close to Ocean Village at this time. However for basic provisions the following should more than meet your needs.
Small Supermarkets
Tesco
Ocean Village Express, Block E, Ranges Court, Southampton SO14 3JS
0845 026 9005
Co-op
117 High Street, Southampton, Hampshire, SO14 2EA
02380 225539
Beer and Wine
Champagne Charley’s (Off License)
12 Canute Rd, Southampton, SO14 3FH
02380 333375
View Supermarkets and Convenience Stores @ Ocean Village in a larger map