Implantable hydrogels should ideally possess mechanical properties matched to the surrounding tissues to enable adequate mechanical function while regeneration occurs. This can be challenging, especially when degradable systems with a high water content and hydrolysable chemical bonds are required in anatomical sites under constant mechanical stimulation, e.g., a foot ulcer cavity. In these circumstances, the design of hydrogel composites is a promising strategy for providing controlled structural features and macroscopic properties over time. To explore this strategy, the synthesis of a new photocurable elastomeric polymer, poly(glycerol-co-sebacic acid-co-lactic acid-co-polyethylene glycol) acrylate (PGSLPA), is investigated, along with its processing into UV-cured hydrogels, electrospun nonwovens and fibre-reinforced variants, without the need for a high temperature curing step or the use of hazardous solvents. The mechanical properties of bioresorbable PGSLPA hydrogels were studied with and without electrospun nonwoven reinforcement and with varied layered configurations, aiming to determine the effects of the microstructure on the bulk compressive strength and elasticity. The nonwoven reinforced PGSLPA hydrogels exhibited a 60% increase in compressive strength and an 80% increase in elastic moduli compared to the fibre-free PGSLPA samples. The mechanical properties of the fibre-reinforced hydrogels could also be modulated by altering the layering arrangement of the nonwoven and hydrogel phase. The nanofibre-reinforced PGSLPA hydrogels also exhibited good elastic recovery, as evidenced by the hysteresis in compression fatigue stress–strain evaluations showing a return to the original dimensions.