We describe a parallel pair of high voltage electric field plates designed and constructed to minimise magnetic Johnson noise. They are formed by laminating glass substrates with commercially available polyimide (Kapton) tape, covered with a thin gold film. Tested in vacuum, the outgassing rate is less than 5 x 10 exp(-5) mbar.l/s. The plates have been operated at electric fields up to 8.3 kV/cm, when the leakage current is at most a few hundred pA. The design is discussed in the context of a molecular spin precession experiment to measure the permanent electric dipole moment of the electron.