The data comes from an annual GP Patient Survey in which patients at 39 GP surgeries in the area were asked if they were still experiencing symptoms more than 12 weeks after they first had Covid-19.
Of the 3,363 respondents in the city, 188 – 5.6% – said they had symptoms of long Covid.
Applying this rate to the population means 12,812 people could be suffering from lingering health problems caused by the virus.
In England, 4.4% of GP patients said they had long Covid symptoms – which can include fatigue, shortness of breath, and heart palpitations – around two million people.
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Long Covid SOS charity called on the Government to stop putting its "head in the sand" and take action to reduce the growing number of long Covid sufferers.
Ondine Sherwood, co-founder of the charity, said: "The Government needs to acknowledge that this is a major issue impacting a significant proportion of the population and that it will lead to a massive burden of ill health on the NHS, on society and the economy.
"The Government needs to stop putting its head in the sand and start to act."
She said stricter infection control measures, more healthcare investment and increased research funding are needed.
The Department of Health and Social Care said more than £50m has gone to help scientists understand the virus's long-term debilitating effects, while the NHS has committed £224 million to support people with ongoing symptoms.