The Long Covid SOS charity has called on the Government to stop "putting its head in the sand" and take action to reduce the growing number of sufferers.
The annual GP Patient Survey polled patients in thousands of practices across England between January and April on various aspects of their health – including 52 in the NHS Shropshire, Telford and Wrekin CCG area.
Patients were asked if they were still experiencing unexplained symptoms more than 12 weeks after they first had Covid-19.
Of the 6,008 respondents in Shropshire, Telford and Wrekin, 277 or 4.5 per cent said they had symptoms of long Covid.
Applying this rate to the latest population estimate for the area as a whole means 19,138 people aged 16 and over in the area could be suffering from lingering health problems.
Across England, 4.4 per cent of GP patients said they had long Covid symptoms – which can include fatigue, shortness of breath, and heart palpitations.
Ondine Sherwood, co-founder of the charity, said most sufferers are unable to obtain any meaningful treatment, and for many even that is not available promptly due to lengthy waiting lists.
She added: "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 Royal College of GPs said post-Covid syndrome is still a relatively new condition, but the prolonged health effects that some experience can have a terrible impact on their lives.
Professor Martin Marshall, chairman, said more resources are needed, including good access to appropriate rehabilitation services in the local community, and more staff working in general practice.
The Department of Health and Social Care said more than £50 million 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.
In the county, a service has been launched for patients with long Covid in December 2020 in a joint project by Shropshire and Telford & Wrekin Clinical Commissioning Groups and Shropshire Community Health NHS Trust.
It aims to provide help and support to local people suffering from Post-Covid Syndrome.