Methane is the second most important anthropogenic greenhouse gas, with a radiative warming of 0.97 [0.74-1.20] W m-2 (Stocker et al., 2013a) and a global warming potential of 21 times that of CO2 over a 100 year timescale (Reay et al., 2010). Its significance to climate change is significant whereas our current understanding and quantification of its sources and sinks lack completeness. This thesis explains the development of novel technique to estimate methane emissions at high spatial resolution. There is a growing need for comparisons between emission estimates produced using bottom-up and top-down techniques. In response to this, an inversion approach, InTEM, was adapted to estimate methane emissions for the East of England at high spatial resolution. InTEM incorporates in situ atmospheric methane measurements and computer dispersion modelling into a statistical technique. Methane emission estimates are inferred using cost function analysis within a simulated annealing method. This thesis presents results covering a two year period (July 2012 - June 2014) in which atmospheric methane concentrations were recorded at 1 - 2 minute time steps at four locations within East Anglia. Precise measurements are obtained using gas chromatographs with flame ionisation detectors (GC-FID) for all sites except one, which uses a Picarro cavity ring down spectroscopy (CRDS) instrument. The UK Met Office's NAME dispersion model is used within InTEM to represent the physical atmospheric processes which occur throughout this period. Methane concentrations are shown to vary over different time frames and are dependent on various meteorological variables, particularly boundary layer height and wind speed. A case study into methane concentration at the Haddenham site shows influence from local landfill sources. Isotopic analysis from whole air samples give a δ13C isotopic signal of -58.3 ±2 ⁄ at the Haddenham site and -59.2 ±2 ⁄ at the nearby landfill. Emission estimates for the East of England are calculated at varying spatial resolutions, on annual and seasonal time frames. County scale methane emission estimates are produced and directly compared with the UK National Atmospheric Emissions Inventory (NAEI). Estimates between the InTEM inventory and the NAEI are shown to be similar in counties close to the observation sites. The Norfolk, Suffolk and Cambridge countries are estimated to produce 80.4 ±3.3 kt yr-1 of methane between June 2013 - May 2014 (NAEI equivalent of 89.6 kt yr-1). Multiple site sensitivity analysis shows that all four sites are necessary for the county methane estimates but coarser estimates can be observed using a sub-selection of sites. Individual site biases were shown to have an impact on 1 -2 site inversions but the four site results minimised these biases.