Extremely shallow under bed storage

[MrsBennetsPoorNerves]

We have a very low IKEA bed. I thought it was called Malm but some Malm beds seem to be higher so not entirely sure. We've had it for 20+ years and I've never been that keen on it but it still seems to be in reasonably good shape so hard to justify replacing it.

One of the things that I really hate about the bed is the limited storage space underneath, but I am wondering if anyone can somehow help me to find some storage bags or boxes that will fit.

I think the bed is 12cm off the ground. I have found some boxes which are exactly 12cm high but suspect these might be just a bit too tight and will be difficult to get in and out, so looking for something around 10-11.5cm high. Preferably needs a lid and I ideally want something that is big enough in terms of length and width to store sheets, pillow cases, duvet covers, towels etc. (I did find some 11.5cm storage boxes but they weren't long/wide enough to fit much at all.)

I feel like I have looked everywhere and can't find anything, but I can't be the only one with a stupidly low ikea bed that has had this problem. Can anyone help?

There's no lid, but if it's that close under the bed, maybe you wouldn't need it - but something like this (or, several of them, as they probably would only fit a couple of sets of bedding in each, at 34x51cm) - only 10cm high.

https://www.ikea.com/gb/en/p/stuk-box-with-compartments-white-90474438/

Or, quite a few wrapping paper cases are approx 12 or 13cm - some of them are fabric, though, so might be slightly squashable, if they are not filled really full.

You could keep searching similar, though, and there might be some shallower ones. Also, many of them are two halves that zip together, and each half has net pockets or velcro etc, so even if it didn't fit when zipped together, you could still lay it out flat, which would let you fit some bedding in each side

https://www.amazon.co.uk/LOVE-STORE-Storage-Gift-Wrap/dp/B0BN28FZKD?source=ps-sl-shoppingads-lpcontext&ref=fplfs&smid=A3P5ROKL5A1OLE&th=1

Or this one might be even too shallow, at only 8.5 cm, and lidded

https://www.nisbets.co.uk/vogue-pp-dough-box-650-x-455-x-85mm/fs998?vatToggle=incvat&cm_mmc=PLA--21488579725&cmmmca1=go21488579725c&kpid=gocmp-21488579725adg-ad-dev-cext-prd-FS998sig-EAIaIQobChMI4L3nn8mBiAMVDIpoCR33ACQEAQYBiABEgJa8fDBwE&plaid=1&gadsource=1&gclid=EAIaIQobChMI4L3nn8mBiAMVDIpoCR33ACQEAQYBiABEgJa8fDBwE

Or another, at 11cm, more square, but I expect you could still fit a set or two of bedding in each one: (also lidded)

https://www.plasticboxshop.co.uk/craft-storage-boxes-c4/14-75-litre-wham-shallow-a3-plastic-storage-box-with-lid-p387/s8046?cid=GBP&glCurrency=GBP&glCountry=GB&ppckeyword=&gadsource=1&gclid=EAIaIQobChMI4L3nn8mBiAMVDIpoCR33ACQEAQYDSABEgKaUvDBwE

Wow, thank you so much for all of those suggestions @BlossomToLeaves - really helpful! One of those has got to work!!