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From the rather bleak description you've provided it doesn't sound like 'decent storage space' to me.Still, as needs must, I suppose.What about some of those larger Really Useful Boxes? That's about all I can think of to be honest. It may cost a bit for a few of the big ones but it may prove cheaper in the long run and they have the added advantage of being stackable and having handles. And you've always got them for other things should you ever move and inherit a non-damp basement.
I'd say your best bet would be the vacuum storage bags . The type designed for storing clothing. These are designed to be moisture resistant.I store a fair amount in my workshop.These have worked quite well for me.For trees and delicate items a box frame does help reduce the compression on the item.
Not being sarcastic but my best recommendation is to move to better quarters. I wouldn't store anything in the environment you've described, not even plastic. The vacuum bags is a reasonable suggestion but I'm not sure they'd survive in the conditions you are dealing with - a lot different that a shop, at least within my reckonings.Good luck, sounds like a challenge.
Have you tried including silica gel packs in the boxes to absorb the moisture? If you can't get the silica gel then rice in a net bag will also work to an extent.
Tell the truth I haven't - worried they'd have to be replaced rapidly. But I should give them a go.
Erm...I think it fair to say they don't seal so much as close.No, they're far from airtight.But maybe you could get some foam (a cut up sleeping mat would give a tight seal) to act as a washer on the closing edges?Looking long term, and not to do with storing gaming materials, if you are going to be in the house for any decent amount of time then it may be worth investing in some proper damp-proofing. Or having it done again if it was done before. I assume the walls are lined, so have them ripped down and a fresh damp-proof layer put in. Ditto the floor.Yeah, a lot of money and a lot of hassle, but it may prove a wise investment for when you sell the house because then it would be a functional room and an extra feature that will increase the value of the property, rather than just a dank space that rots everything and gives people pneumonia.
There are types you can recharge by placing in a low temperature oven for a couple of hours to remove accumulated water. Also there are ones which change colour when saturated so you know when to change them out - great if you have transparent bins.
emergency/survival food storage containers generally have airtight seals. add some of the rechargeable desiccant packets/bags.