Endangered British vegetables, such as purple carrots, will be grown on the roof of the Crouch End site, and the produce sold in the store below.
All materials used in the Food from the Sky initiative will be recycled, with the produce grown in troughs made from old pallets. A webcam will chart the progress of the project, which will be run by volunteers and store staff.
The scheme was thought to be a "world first", said store manager Neil Duggard, and seeds were already being propagated in the corner of the store's car park in anticipation of the opening of the garden.
l Squirrel meat has been on sale in the store for the past four weeks, and had attracted "huge interest", said Duggard. He admitted, however, that many customers were asking just to look at it rather than buy it.