National greenhouse gas inventories (GHGIs) are submitted annually to the United Nations Framework Convention on Climate Change (UNFCCC). They are estimated in compliance with Intergovernmental Panel on Climate Change (IPCC) methodological guidance using activity data, emission factors and facility-level measurements. For some sources, the outputs from these calculations are very uncertain. Inverse modelling techniques that use high-quality, long-term measurements of atmospheric gases have been developed to provide independent verification of national GHGIs. This is considered good practice by the IPCC as it helps national inventory compilers to verify reported emissions and to reduce emission uncertainty. Emission estimates from the InTEM (Inversion Technique for Emission Modelling) model are presented for the UK for the hydrofluorocarbons (HFCs) reported to the UNFCCC (HFC-125, HFC-134a, HFC-143a, HFC-152a, HFC-23, HFC-32, HFC-227ea, HFC-245fa, HFC-43-10mee and HFC-365mfc). These HFCs have high global warming potentials (GWPs), and the global background mole fractions of all but two are increasing, thus highlighting their relevance to the climate and a need for increasing the accuracy of emission estimation for regulatory purposes. This study presents evidence that the long-term annual increase in growth of HFC-134a has stopped and is now decreasing. For HFC-32 there is an early indication, its rapid global growth period has ended, and there is evidence that the annual increase in global growth for HFC-125 has slowed from 2018. The inverse modelling results indicate that the UK implementation of European Union regulation of HFC emissions has been successful in initiating a decline in UK emissions from 2018. Comparison of the total InTEM UK HFC emissions in 2020 with the average from 2009-2012 shows a drop of 35 %, indicating progress toward the target of a 79 % decrease in sales by 2030. The total InTEM HFC emission estimates (2008-2018) are on average 73 (62-83) % of, or 4.3 (2.7-5.9) Tg CO.sub.2 -eq yr.sup.-1 lower than, the total HFC emission estimates from the UK GHGI. There are also significant discrepancies between the two estimates for the individual HFCs.