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We present a mass balance approach to estimate the seasonal and annual budgets of carbon dioxide (CO2) and methane (CH4) of the United Kingdom (excluding Scotland) and the Republic of Ireland from concentration measurements taken on a ferry along the east coast of the United Kingdom over a 3-year period (2015-2017). We estimate the annual emissions of CH4 to be 2.55 +/- 0.48 Tg, which is consistent with the combined 2.29 Tg reported to the United Nations Framework Convention on Climate Change by the individual countries. The net CO2 budget (i.e. including all anthropogenic and biogenic sources and sinks of CO2) is estimated at 881.0 +/- 125.8 Tg, with a net biogenic contribution of 458.7 Tg (taken as the difference between the estimated net emissions and the inventory value, which accounts for anthropogenic emissions only). The largest emissions for both gases were observed in a broad latitudinal band (52.5-54 degrees N), which coincides with densely populated areas. The emissions of both gases were seasonal (maxima in winter and minima in summer), strongly correlated with natural gas usage and, to a lesser extent, also anti-correlated with mean air temperature. Methane emissions exhibited a statistically significant anti-correlation with air temperature at the seasonal timescale in the central region spanning 52.8-54.2 degrees N, which hosts a relatively high density of waste treatment facilities. Methane emissions from landfills have been shown to sometimes increase with decreasing air temperature due to changes in the CH4-oxidising potential of the topsoil, and we speculate that the waste sector contributes significantly to the CH4 budget of this central region. This study brings independent verification of the emission budgets estimated using alternative products (e.g. mass balance budgets by aircraft measurements, inverse modelling, inventorying) and offers an opportunity to investigate the seasonality of these emissions, which is usually not possible.