Most insurance companies are reluctant to insure 'collections' of records, CD's (or even VHS tapes in the past)!!
Like Chris, I have mine covered by 'all risks' house contents policy, but have a database of my collection that I have submitted to the insurers.
Insurers, from my personal experience, won't usually accept a quantitative value based on your expectations, especially as some records/CDs may individually be quite valuable (or expensive to purchase). So, they would subsequently apply a value based on 'numbers held', ie: 1000 discs or 2000 records and would, I expect, try to get away with reimbursing the number in collection multiplied by (eg) £2.00 each, which may not be of any use to you if you believe you have a quantity of valuable, or irreplaceable ones!
I've always found it difficult to insure the hi fi and the collections when a lot of companies apply individual limits to components, and won't entertain a 'collection', as such!
I currently don't stream or download, but how do those that do, insure a hard drive full of material that they have collected for years, or even go about replacing it in the event of a 'total loss'?
G
Technics SL1000R, DynavectorXV1t, Garrard 401, Jelco SA750LB, Decca Reference, ATVM750SH, AT33Mono, Hana Umami Red, Reimyo CDP777, EarYoshino 912, Ear Yoshino 509s, JBLK2 SL5800s, ART Dram interconnects / speaker cables.