From what I hear cockers are hoarders, mine certainly is, and has earnt herself the fitting nickname of 'maggie magpie'. She was given this name by mother because she will steal things and hoard them in her bed...lol. I guess this is a pretty natural instinct for a gundog
However, there are some items she knows she must leave, e.g. food, shoes, hamsters etc, and she doesnt touch them. If there is an item she is not allowed I take it to her, and tell her 'leave it', as she looks away I reward her. She now knows 'leave it' and as she sniffs something she is not allowed I tell her, "no, leave" and she does so. When she was a baby she didnt fully understand leave, and so i had to use my voice to let her know that i didnt want her to touch the object. She rarely picks things up in the house now even when I am not there.
If she picks up something I haven't told her to leave, I dont tell her off, I just calmly ask her to fetch it and give it to me, trading it for a treat or toy that she is allowed.
This suggestion may not work for all dogs, but it has worked very well for me (so far) and I hope it may work for someone else here also.
sportsmonki