We carry out three-dimensional smoothed particle hydrodynamics simulations to study the role of gravitational and drag forces on the concentration of large dust grains (St > 1) in the spiral arms of gravitationally unstable protoplanetary discs, and the resulting implications for planet formation. We find that both drag and gravity play an important role in the evolution of large dust grains. If we include both, grains that would otherwise be partially decoupled will become well coupled and trace the spirals. For the dust grains most influenced by drag (with Stokes numbers near unity), the dust disc quickly becomes gravitationally unstable and rapidly forms clumps with masses between 0.15–6M⨁. A large fraction of clumps are below the threshold where runaway gas accretion can occur. However, if dust self-gravity is neglected, the dust is unable to form clumps, despite still becoming trapped in the gas spirals. When large dust grains are unable to feel either gas gravity or drag, the dust is unable to trace the gas spirals. Hence, full physics is needed to properly simulate dust in gravitationally unstable discs. Dust trapping of large grains in spiral arms of discs stable to gas fragmentation could explain planet formation in very young discs by a population of planetesimals formed due to the combined roles of drag and gravity in the earliest stages of a disc’s evolution. Furthermore, it highlights that gravitationally unstable discs are not just important for forming gas giants quickly, it can also rapidly form Earth mass bodies.