We present a straightforward low cost liquid phase deposition method to coat arbitrary-shaped dielectric substrates with uniform electron beam sensitive polymer films. Furthermore, we investigate the use of electron beam lithography to pattern the coated pre-form substrates. The polymers studied are poly-methyl-methacrylate with different molecular weights, poly(methyl methacrylate-co-ethyl acrylate) and methyl methacrylate. The polymer coverage over the whole surface area is shown to be uniform and the thickness of the film dependent on the concentration of the polymer liquid used. As the uniform polymer layer is deposited on non-flat surfaces, we show that with an electron beam various surfaces, e.g. microlens arrays, can be re-patterned accurately with nanoscale features. Furthermore, we show the required dose for electron beam exposure to be dependent on the concentration and on the molecular weight of the polymer used. (Some figures in this article are in colour only in the electronic version)