I won't go into too much detail here, but I recently decided to rent a secure storage unit to store my Lego in while I move house (hopefully it'll sell quicker if it's not rammed full of Lego!).
I asked my home contents insurance provider to give me a quote for insuring my Lego collection in the storage unit. Bear in mind at this point that my insurance company were previously unaware of my collection - I suspect like many AFoLs I just assumed it would be covered under normal contents insurance, as long as it didn't exceed the total insured value.
They got back to me a couple of days later, and said that it was a bit complicated. To insure the storage unit I'd have to take out a separate policy with them, which was quite expensive (i.e. a rip-off).
But that wasn't the killer.
Apparently, once I moved my Lego back into my house, I was to tell them I had, because at that point they would cancel my current insurance policy. Basically, although they were willing to insure my Lego in a secure storage unit, it turns out that they weren't willing to do so if it was in my home!
Thankfully I was quickly able to get a new insurance policy with my bank, who were happy to insure my collection in my house, and gave me a very reasonable price for insuring the storage unit too.
So the moral of the story is, don't just assume your insurance provider will automatically insure your collection, because some won't!