Many volcanoes show continuous but variable deformation over timescales of years to decades. Variations in uplift rate are typically interpreted as changes in magma supply rate and/or a viscoelastic response of the host rock. Here we conduct analogue experiments in the laboratory to represent the inflation of a silicic magma body at a constant volumetric flux, and measure the chamber pressure and resulting surface displacement field. We observe that dyke intrusions radiating from the magma body cause a decrease in the peak uplift rate, but do not significantly affect the spatial pattern of deformation or spatially averaged uplift rate. We identify 4 distinct phases: 1) elastic inflation of the chamber, 2) a gradual decrease in the rate of uplift and pressurisation, associated with the formation of visible cracks 3) propagation of a dyke by mode 1 failure at the crack tip and 4) a pressure decrease within the chamber. Phase 2 can be explained by either a) crack damage, which reduces the elastic moduli of the surrounding rock or b) magma filling pre-existing cracks. Thus these experiments provide alternative mechanisms to explain observed variations in uplift rate, with important implications for the interpretation of deformation patterns at volcanoes around the world.