Structured surfaces give rise to novel and potentially useful properties such as controllable wettability and structural colour. Here, we demonstrate structured surfaces via reversible surface wrinkling in liquid crystal elastomers (LCEs). A thin polymer film deposited on top of a shape-responsive LCE exhibits a reversible, periodic surface wrinkling pattern in response to temperature changes. The orientation of the wrinkles depends on the orientation of the nematic director and the temperature at which the bilayer is prepared, and the wrinkles can be re-oriented in a single sample by heating or cooling the sample above or below the preparation temperature. We show that this bilayer system can be used to measure the modulus of nanoscale thin poly(styrene) films deposited on the LCE. Additionally, when a micron-thick polymer film is deposited on top of an LCE, the bilayer exhibits reversible curling with temperature. This system provides a simple method for measuring the mechanical properties of thin polymer films without the need for clamping and mechanical stretching and provides a new approach to generate reversible, microstructured surfaces.