This dataset provides UK maps of baseline prior uncertainty (UQ) in fluxes of Greenhouse Gases (GHGs) carbon dioxide, CO2 (2014-15) and methane, CH4 (2015). Spatial maps of these GHG emissions are produced annually in the National Atmospheric Emissions Inventory (NAEI) but it is important to quantify uncertainty in these maps. These uncertainty estimates come from sectoral uncertainty data provided by the NAEI. Here, we propagate the uncertainty in the maps for each of the sectors contributing to the emissions using a Monte Carlo method, in order to quantify the uncertainty in the total emissions spatially. The Monte Carlo method employed here uses a novel approach (Nearest Neighbour Gaussian Process) to make calculations computationally affordable. These estimate the influence on the overall uncertainty of unknown errors in the model structure. Further details of the methodology used here can be found in the supporting documentation included with this data. In the near term, this methodology will be used and developed further in the NERC-funded project, DARE-UK (NE/S003614/1), to update UQ in maps of CO2 and CH4 for the UK. For that work and in general, it is useful to have a baseline prior uncertainty quantification against which future UK maps of uncertainty in CO2 and CH4 fluxes can be compared. Full details about this dataset can be found at https://doi.org/10.5285/739c65a5-12c0-439b-bbcd-1252a4086e87