Bandgaps in two- and three-dimensional photonic crystals are hard to achieve due to the limited contrast in the dielectric permeability available with conventional dielectric materials. The situation changes for periodic arrangements of scatterers consisting of materials with a Drude-like behaviour of the dielectric function. We show for two-dimensional square and triangular lattices that such systems have in-plane complete photonic bandgaps (CPBGs) below infrared wavelengths. Of the two geometries, the optimal one for ideal Drude-like behaviour is a square lattice, whereas for Drude-like behaviour in silver, using experimental data (Palik E D 1991 Handbook of Optical Constants of Solids vol 1 (San Diego: Academic)), the optimal geometry is a triangular lattice. If the lattice spacing is tuned to a characteristic plasma wavelength, several CPBGs open in the spectrum and their relative gap width can be as large as 36.9% (9.9% in a nonabsorptive window) even if the host dielectric constant ε_h = 1. Such structures can provide CPBG structures with bandgaps down to ultraviolet wavelengths.