A carcass structure for a vehicle wheel tyre includes at least one carcass ply comprising thread elements substantially disposed transversely of a circumferential extension of the carcass structure, and at least one pair of annular reinforcing structures disposed close to respective inner circumferential edges of the at least one carcass ply. Each of the annular reinforcing structures includes at least one first circumferentially-inextensible annular insert formed of at least one first elongated element extending in concentric coils, and at least one second circumferentially-inextensible annular insert formed of at least one second elongated element extending in concentric coils. The at least one carcass ply has end flaps each turned back around an inner circumferential edge of a respective first annular insert and each axially interposed between respective first and second annular inserts. A method of manufacturing the carcass structure is also disclosed.