Electrospinning is the process of choice allowing the preparation of nanofibrous materials from a solution usually based on a high molar mass polymer. The solution must bring enough chain entanglements to avoid any breaking or Rayleigh instability of the electrospun jet resulting thus in the deposition of a continuous and regular solid nanofibre. It has been however shown that some few non-polymeric molecules can be electrospun without using a carrier polymer. We demonstrate here the case of tannic acid. Indeed, it was possible to electrospin this molecule solubilised in a mixture of water and ethanol as well as in pure water. Rheology, dynamic light scattering and cryo-TEM highlight the formation of tannic acid aggregates in solution. Above a critical concentration, these aggregates form a supramolecular interconnected network strong enough to allow the electrospinning of a continuous and regular nanofibre. The resulting nanoweb is mechanically stable and can be handled and wrapped. Furthermore, as opposed to the other small molecules for which polymer-free electrospinning was also demonstrated, tannic acid nanowebs can be efficiently cross-linked in water either by oxidative reaction with sodium periodate or, most interestingly, with FeIII by a combination of oxidative reaction and the formation of coordination complexes. The proposed electrospinning and cross-linking strategy is easy, of low cost, and scalable and uses non-toxic solvents as well as biocompatible and biofunctional molecules. Furthermore, thanks to the chelation capacity of tannic acid having the ability to coordinate with a wide variety of metals, hybrid smart nanowebs can be envisaged for diverse applications such as biomedical, catalysis as well as environment.