The formation and propagation of aggregates of the tau protein in the brain are associated with the tauopathy group of neurodegenerative diseases. Different tauopathies have been shown to be associated with structurally distinct aggregates of tau. However, the mechanism by which different structural folds arise remains poorly understood. In this study of fibril formation by the fragment tau-K18 of tau, it is shown that the Lys 280 → Glu mutation in the variant tau-K18 K280E forms fibrils that are morphologically distinct from those formed by wild-type (wt) tau-K18. The mutant fibrils appear to have two protofilaments twisted around each other, whereas the wt fibrils are straight and appear to have a single protofilament. Modeling the kinetics of seeded aggregation, using a simple Michaelis-Menten-like mechanism, reveals that the two morphologically distinct fibrils are elongated with different catalytic efficiencies. Surprisingly, when the elongation of monomeric tau-K18 is seeded with tau-K18 K280E fibrils, it is seen to be inhibited at high monomer concentrations. Such inhibition is not seen when elongation is seeded with tau-K18 fibrils. The mechanism of inhibition is shown to be describable as uncompetitive inhibition, in which a transient dimeric form of tau-K18 acts as an uncompetitive inhibitor. Importantly, a dimeric form of tau-K18 is seen to be populated to a detectable extent early during aggregation. A covalently linked tau dimer, with an inter-molecular disulphide linkage, is shown to be capable of acting as an inhibitor. In summary, a quantitative kinetic approach has provided an understanding of how the formation of distinct structural folds of tau fibrils can be modulated by mutation and how the elongation of one fibril type, but not the other, is inhibited by a transiently formed dimer.