A new dynamical model for the formation of dominant cluster galaxies and powerful radio sources at high redshifts is proposed. In this model, powerful high-redshift radio galaxies are assumed to represent an early stage in the formation of massive cD galaxies in the centres of rich clusters, corresponding to an epoch when these galaxies were being built via mergers of smaller gas-rich protogalactic units. It is argued that in many cosmogonies such mergers will not occur haphazardly, but rather will proceed in a coherent or 'organized' manner along preferred axes which are related to large-scale anisotropies in the primordial density field. As a consequence of this anisotropic formation process, these galaxies are quite prolate in shape and have a built-in 'memory' of their surroundings, even at high redshifts. Such a formation scenario can account quite naturally for the observed shapes and kinematics of cD galaxies today, as well as their tendency to be aligned with the major axis of their parent cluster and the galaxy distribution on much larger scales. Frequent mergers during this early formation phase are likely to provide an abundant source of gas-rich material. Cold gas falling into the prolate potential well of these burgeoning galaxies will quickly settle into a disc whose angular momentum vector is aligned with the major axis of the (proto)galaxy mass distribution. Angular momentum loss during this settling process results in an inward flow of gas towards the centre of the young galaxy, which provides a plentiful source of material for both the creation and feeding of a central black hole. It is argued that under these circumstances the black hole spin axis will align with the angular momentum vector of the fuelling accretion disc, and hence its orientation will ultimately be determined by the intrinsic shape and orientation of the host galaxy. In the standard 'twin-exhaust' model for active galactic nuclei, the radio jets are expected to emanate along the black hole spin axis, and thus will tend to align with the major axis of the mass distribution in these prolate protogalaxies. It is for this reason that the extended optical and infrared components of powerful high-z radio galaxies are often closely aligned with the radio axis. The model proposed here implies a truly remarkable coherence of structures from the central engines in active galactic nuclei to the large-scale structure of the Universe. Several low-redshift analogues to powerful high-redshift radio galaxies are discussed and shown to exhibit properties that suggest that they may indeed have formed in the manner described here. A number of testable predictions of this model are also made.