Advocates of Britain remaining in Euratom say it remains unclear what the bill will say about the treaty — if anything — and some members of Parliament, including some of Mrs. May’s fellow Conservatives, could revolt over the issue. Underlining those concerns, this week Dominic Cummings, director of the campaign to leave the European Union, turned to Twitter to castigate what he labeled “government morons” who want to withdraw from the treaty.

Among the other voices expressing alarm is Dr. Nicola Strickland, president of the Royal College of Radiologists. Noting that Euratom regulates the trade of radioactive isotopes of the type used to diagnose and treat cancer, she said she was worried that the access to these materials could be undermined if Britain left the treaty.

“The Royal College of Radiologists, like others in medicine and industry, is seriously concerned about continued access to these materials if we leave the Euratom treaty under Brexit,” Dr. Strickland said in a statement. She said she also wanted assurances that radiation safety laws and rules governing trade, enshrined in the Euratom treaty, would continue.

Rupert Lewis, a spokesman for the Nuclear Industry Association, which represents the British civil nuclear industry, said that if Britain withdrew from Euratom, it could find itself sidelined from vital and lucrative nuclear trade agreements with the United States, Canada and Japan. And without a replacement agreement, he said, Britain’s trade in nuclear products and services could slow down or come to halt, potentially threatening some of the 65,000 jobs in its nuclear sector.

Also at risk, Mr. Lewis said, was pioneering international fusion research underway at a test reactor in Culham, Oxfordshire, the world’s largest operational nuclear fusion device, which depends on funding by Euratom members. Some experts have estimated that if Britain leaves Euratom and the device is decommissioned, the loss in funding could run to hundreds of millions of dollars.