Hi Jules,
Yes, the shop is plenty good enough for most things and is about 14 seconds gentle walk from the Barn! Generally they discourage people taking food supplies in order to keep the shop viable and that seems entirely reasonable.
If you simply must have a particular brand of something a bit esoteric (Goggin’s olde-world-style matured Damson chutney maybe?) then perhaps smuggle a jar of that on board but otherwise I really wouldn’t bother.
Fresh meat and veg is in good supply each time a boat arrives (3 times a week) but does tend to run out a day or two later. They do however bake bread on the Island! Buy it when its on the shelf because it won’t be there still later. For fresh stuff generally, a bit of strategic shopping works well but resorting to the shop’s well-stocked freezers works as well. Too much advance purchasing will exceed the capacity of the Barn’s fridges!