The British government has a policy of not commenting on its special forces, in contrast to other countries including the US.
The UK has been vociferous in its support of Ukraine, and is the second largest donor after the US of military aid to Kyiv.
US Defense Secretary Lloyd Austin said the Department of Justice had opened a criminal investigation and he was determined to find the source of the leak.
"We will continue to investigate and turn over every rock until we find the source of this and the extent of it," he said.