Department for Business, Energy and Industrial Strategy (BEIS) figures show that CO2 emissions in the area dropped by 5.9% in 2019 – the latest available data – compared to the year before.
Homes were responsible for emitting the largest amount of CO2 in the area – 411,000 tonnes – but that has dropped by 30.6% over a decade.
Between 2009 and 2019, overall CO2 emissions in the city dropped by 28.3%.
Nationally, 360 of 379 local authority areas saw a decrease in emissions in 2019, with an overall drop of 3.6% owing to a change in the fuel mix for electricity generation, greater use of renewables and a drop in the use of coal, according to BEIS.
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A spokesman for the Zero Carbon campaign said: "To reach net zero emissions by 2050 and deliver our even more ambitious target to reduce emissions by 78% by 2035, we need to decarbonise much further, faster and across a far greater section of our economy.
Friends of the Earth said local authorities do not have the resources to decarbonise some of the most polluting sectors such as housing and transport, due to budget cuts.
A BEIS spokesman said: “The UK was the first major world economy to commit to ending our contribution towards climate change by 2050 and we continue to make great strides towards that target thanks to the continual effort and dedication of the local authorities."