Some home contents insurance does allow record collections to be covered in house for usual fire, theft, water etc to but not all covered outside the house. It’s harder though now from many companies - I just had mine refused after several years with no claims so had to go for a more expensive bespoke firm via a broker. It’s important to have the value named on the policy and the approx number of records. You don’t have to list them all. They may also allow a smaller amount and number to be insured outside the house.
I have heard there are specialist DJ equipment policies including records.