In our shed we kept a couple of unused bags of compost from last year and they had all been torn open by rats who are partying in the shed in the winter when we don't go in there for several days or weeks. I doubt squirrels could get in there. To store compost I now empty them into large hard plastic outdoor bins that are about a foot shorter than a council wheely bin.
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https://www.amazon.co.uk/GREEN-FEEDING-BUCKET-GARDEN-FLEXIBLE/dp/B01MA3IVL9
Looks like this