I had my garage done a few years ago and they took my fishing bag and a rusty drill I was glad to see the back of. I 'phoned my Insurance Company (can't remember their name unfortunately) and they tried to fob me off with "equivalents", like replacing my Avon Scales with a set of Little Sampsons. I had my name and 'phone on the inside flap of the bag and I got a call to say that it had been dumped and all my gear was still in it, the only thing missing was my £20 emergency fund,
My mate is always selling on Facebook Market Place and not long after showing a shifty looking character around, he got done big time and in a professional hit, they made off with £8,000 of quality gear. He was with Lloyd's and couldn't fault them for the way they dealt with the claim.
I got a heavy duty padlock bolted to the ground and an internal Yale alarm - my mate's alarm did go off but they filled it with expanding foam.
I don't really trust Insurance Companies, they are normally quick to take your money and slow to pay out and even then, the bare minimum.
Beef up your security as much as possible without drawing too much attention to the shed.
If the worst does happen, don't expect the Police to come rushing round, they will only want to give you a crime number!