We present results of a 3-month combined X-ray/UV/optical monitoring campaign of the Seyfert 1 galaxy NGC 6814. The object was monitored by Swift from June through August 2012 in the X-ray and UV bands and by the Liverpool Telescope from May through July 2012 in B and V. The light curves are variable and significantly correlated between wavebands. Using cross-correlation analysis, we compute the time lag between the X-ray and lower energy bands. These lags are thought to be associated with the light travel time between the central X-ray emitting region and areas further out on the accretion disc. The computed lags support a thermal reprocessing scenario in which X-ray photons heat the disc and are reprocessed into lower energy photons. Additionally, we fit the lightcurves using CREAM, a Markov Chain Monte Carlo code for a standard disc. The best-fitting standard disc model yields unreasonably high super-Eddington accretion rates. Assuming more reasonable accretion rates would result in significantly under-predicted lags. If the majority of the reprocessing originates in the disc, then this implies the UV/optical emitting regions of the accretion disc are farther out than predicted by the standard thin disc model. Accounting for contributions from broad emission lines reduces the lags in B and V by approximately 25% (less than the uncertainty in the lag measurements), though additional contamination from the Balmer continuum may also contribute to the larger than expected lags. This discrepancy between the predicted and measured interband delays is now becoming common in AGN where wavelength-dependent lags are measured.