(btw, 1600-1800 is considered modern: medieval is usually reckoned to end in 1485 in England)

Until this time most food shopping was probably done at the market where traders would set up with their wares, moving from one town or locality to the next. But early structures have survived in some provincial towns and shops were plentiful in London by 1598, when Stow wrote:

Men of trades and sellers of wares in this City have often times since changed their places, as they have found their best advantage.... the Pepperers and Grocers of Sopers Lane, are now in Bucklersbury, and other places dispersed.... The Stockfishmongers in Thames Street: wet Fishmongers in Knightriders Street, and Bridge Street... Vintners from the Vintry into divers places.... Cooks, or Pastelers for the more part in Thames Street, the other dispersed into diverse parts. Poulters of late removed out of the Poultry betwixt the Stocks and the great Conduit in Cheap into Grass Street, and Saint Nicholas Shambles...

You'll notice pepperers, specialising in the spices of Asia and other parts and already reflecting increased long-distance supplies. But as late as 1620 Europe's total imports of pepper and fine spices are estimated at only 4,500 tons, 50g per head per year; English imports in 1700 are reckoned at £100,000, or 4½d per person. Coffee and later tea were already making their mark, but the big change was 18th-century sugar, estimated consumption of which rose in the 18th century from 4lb to 18lb per head.

Shops were initially identified by symbols outside the storefront, usefully when literacy remained limited. Press advertising got under way in the 18th century, but food retailers seem not to have been prominent until the 19th.

it would be helpful if you define a more precise time period.