Provided are a computer program product, system, and method for processing a read operation for a target block of data. A read operation for the target block of data in target storage is received, wherein the target block of data is in an instant virtual copy relationship with a source block of data in source storage. It is determined that the target block of data in the target storage is not consistent with the source block of data in the source storage. The source block of data is retrieved. The data in the source block of data in the cache is synthesized to make the data appear to be retrieved from the target storage. The target block of data is marked as read from the source storage. In response to the read operation completing, the target block of data that was read from the source storage is demoted.