The Phoenix by Sylvia Townsend Warner

Lord Strawberry, a nobleman, collected birds. He had the finest aviary in Europe, so large that eagles did not find it uncomfortable, so well laid out that both humming birds and snow-buntings had a climate that suited them perfectly. But for many years the finest set of apartments remained empty, with just a label saying: "PHOENIX. Habitat: Arabia."
Many authorities on bird life had assured Lord Strawberry that the phoenix is a fabulous bird, or that the breed was long extinct. Lord Strawberry was unconvinced: his family had always believed in phoenixes. At intervals he received from his agents (together with statements of their expenses) birds which they declared were the phoenix but which turned out to be orioles, macaws, turkey buzzards dyed orange, etc., or stuffed cross-breeds, ingeniously assembled from various plumages. Finally Lord Strawberry went himself to Arabia, where, after some months, he found a phoenix, won its confidence, caught it, and brought it home in perfect condition.