I have an Asgard Shed.
But...
One of the best bits of advice was ever given was to only buy Defacto 5 star insurance it's just a better quality product and for me was lass than £5 more expensive than a 2 star policy.
When getting quotes in, which I do every year I just rummage through the ones I like until I find the one with the best and least onerous terms. Then, crucially I feel, I email or check with them to make sure they meet my needs (essentially locked inside the shed).
Last year I was with Tesco on their better policies, this year I think it's Aviva. Usually comes in at about £135 for part of a house and contents. I think about £2.20 a week is stonking value.
Last year someone was threating to make a claim against me and it was a comfort to know my max exposure was about £50.
Winston Churchill is quoted as saying.....
"If I had my way, I would write the word ‘insure’ over every door of every cottage and upon the blotting pad of every public man, because I am convinced that, for sacrifice that are conceivably small, families can be secured against catastrophes which otherwise would smash them forever.”
I'd temper that against the nonsense policies and extended warranties that we see today.