When Lucy first meets Mr Tumnus he is carrying shopping packages. I don't recall any mention of Narnian cities near the Lamp-post though so where has he got the packages from?
1) The White Witch only had control of Narnia, not Archenland or Calormen. Goods may have been imported/smuggled in from those countries. These probably are also the Narnians' main food suppliers since the Witch's magical winter is limited to the Narnian borders.
2) In Prince Caspian, we're told that the Dwarves had a much easier time under the Witch's rule than most of the beasts. Dwarves are master crasftsmen, so they could be supplying goods to the Narnian economy.
3) Narnia doesn't seem to have any major towns outside the castles until the founding of Beruna during the Telmarines' time. And we know there aren't any humans in Narnia. But in the Silver Chair, we learn that Marshwiggles live in a village; to me, this suggests there might be villages with other creatures, or possibly regular open-air markets.
4) We can probably rule out any trade with the various islands. Hags, ogres, wolves, and the like just don't strike me as sea-farers.
Really, though, it's never actually addressed.
I can think of a couple of possible answers to this one.
Maybe the same place as Mrs Beaver got her sewing machine from?
Or, put less snarkily: by the time he wrote The Lion, the Witch, and the Wardrobe, Lewis didn't seem to have the whole Narnia legendarium built up in his head. He included things like sewing machines, lamp-posts, and shopping parcels which don't really seem to fit into the magical world of Narnia. The lamp-post, of course, was given an explanation in The Magician's Nephew, but the sewing machine and the shopping parcels may just need to be waved away as anachronisms.
Alternatively, are you sure they were shopping packages specifically? Maybe they were just things he'd got from an acquaintance living in the woods which had been wrapped up in paper to protect them from the snow. (It's been a long time since I read the Narnia books, so I may be wrong on this one, if the description given in the book contradicts me.)