In this paper we delineate the consequences of field-dependent solvent polarization in the electric double layer (EDL) electrostatic potential distribution, and the effective EDL thickness in narrow nanofluidic confinements with thick (or overlapping) EDLs. The EDL, formed at the interface between a charged substrate and an electrolyte solution, induces a large electric field spanning across few nanometer distances from the interface. As a result, a polar solvent like water gets polarized, making its relative permittivity a function of the EDL electric field. This affects the overall EDL electrostatic potential distribution and most importantly, leads to a significant reduction of the effective EDL thickness, with the extent of the reduction being dictated by the value of field independent EDL thickness, strength of the solvent polarization, and the substrate-liquid interfacial electrostatic potential. Such a finding will necessitate redefining the classical EDL thickness, which will be of overwhelming significance in nanofluidic transport.