Did you leave them in the ground until their skins were hardened off a bit? (well after the tops die back)
After that, get them DRY. I lay mine out on newspaper and run a fan over them for a few days, turning them over once (I grow close to 200 pounds of potatoes -- so this *can* be done with a big harvest!)
After that you want cool, good air circulation, some humidity but not too much, and DARK. And you definitely don't want freezing. How dark/not too humid/above freezing all winter is your shed?

So I'd say no on the shredded paper -- would only block air flow.
Galvanized bin is okay -- But I use plastic laundry baskets with open slats to maximize air flow. To maximize space you could use stackable bins or shelves to put the bins on.

I'm sure others will have ideas for you, too.
Can't lose the potatoes!!!

This post was edited by elisa_Z5 on Fri, Jul 18, 14 at 9:35

If it is cool where you live, store them in the ground for quite a while unless the weather is extra wet and the soil soggy.

My parents, experts at feeding us for a year with a short summer's crops, would store potatoes right out of the field in an unheated (but not freezing) dry dark cellar in wooden barrels/kegs all winter. This was in New Hampshire (north east USA seacoast) where the winter temps pretty much mirrored the southern UK. By spring (late April) the remnants were softening and sprouting and became seed potatoes. I don't know the variety.

>his was in New Hampshire (north east USA seacoast) where the winter temps pretty much mirrored the southern UK

Really? New Hampshire is milder than the rest of New England? I never knew that.

I don't grow potatoes but afaik they do not store well for very long in the ground in the British Isles. It's just too wet and they rot or get eaten by slugs. RHS says up until October if it isn't to wet.

Here is a link that might be useful: Storing potatoes

I store potatoes in bushel barrels in the garage. I put a layer of hay in first, then potatoes and so on til its full, ending with some hay. No problems so far, and they all keep.

"This was in New Hampshire (north east USA seacoast) where the winter temps pretty much mirrored the southern UK" Not sure that's accurate. I believe NH winters are much colder, even on the coast.