The pandemic has dented the U.K. private-hospital business, a niche real-estate development sector targeting wealthy patients and those with private insurance plans.

While most citizens of the U.K. get medical care from the government-funded National Health Service, private companies, many of them U.S.-based, have developed private hospitals that operate about 1,300 beds in London.

Revenue has fallen because Covid-19 restrictions have greatly limited a major source of demand: patients from Asia, the Middle East and other countries, according to analysts. The decline has raised questions about future development projects.

Healthcare industry participants are now watching the expected opening early next year of a 184-bed hospital in a converted office building by the Cleveland Clinic. The Cleveland, Ohio-based healthcare provider operates in Ohio, Florida, Nevada, Toronto and Abu Dhabi, and established a beachhead in London this year with an outpatient facility.

Adding 14% to capacity at a time of lagging demand will likely create a glut, according to Ted Townsend, who writes an annual report on private healthcare in London for business analyst LaingBuisson.

“While overseas patients will come back to London, the overall number of patients won’t be growing,” said Mr. Townsend, who estimated the Cleveland Clinic is spending about £1 billion, equivalent to around $1.37 billion, on the London project. “We will have a big overcapacity problem.”

The hospital is in the upscale Belgravia neighborhood, and within sight of Buckingham Palace.

A spokeswoman for the Cleveland Clinic said its high world rankings and emphasis on research and technology would win it patients. “We believe London is, and will remain, one of the leading healthcare centers in the world and represents a great opportunity,” she said.

A glut would be a disappointment for some developers that specialize in medical buildings and landowners with vacant sites. The pandemic has already put a damper on other types of downtown development, particularly office buildings because of the success of remote working while the country has been on lockdown.

Mr. Townsend believes other medical groups will be eager to see how the Cleveland Clinic performs before stepping into the crowded market. “I am sure the U.K. comes up on everyone’s acquisition scan once a year, but groups running general hospitals will be thinking: ‘Let’s wait and see.’ ”

The U.K.’s National Health Service, launched in 1948, soon after World War II, received £212.1 billion in government funding between April 2020 and April 2021, including an additional £60 billion to fund its response to the pandemic.

Private-hospital development boomed in the 1970s, and today 28 inpatient facilities are operating in London.

Private-hospital revenue in London had been growing steadily before the pandemic, to £1.8 billion in 2019 from £1.4 billion in 2014, according to Mr. Townsend. He estimates that revenue fell 14% to £1.6 billion in 2020.

Some private-hospital companies have taken a cautious approach to British expansion. The Mayo Clinic, based in Minnesota, in 2020 opened an outpatient clinic that a spokeswoman described as a “gateway” to virtual consultations with Mayo’s 4,000-or-so U.S.-based physicians.

HCA Healthcare, of Nashville, Tenn., has been more aggressive. It has six private hospitals in London and operates a string of clinics as well as wards in several NHS hospitals. Its U.K. total income in 2019 was £670 million.

HCA’s next project is a £100 million, 50-bed hospital under construction in the regional city of Birmingham that is to open next year. The company didn’t respond to a request for comment.

The Cleveland Clinic signed a lease on the 325,000-square-foot, 1950s-era office building it converted back in 2015, but permits to remodel the building weren’t awarded until 2017. The hospital originally was scheduled to open this year, but work was delayed during the pandemic.

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