"We are reviewing further measures," writes British Foreign Minister James Cleverly on Twitter.
The news of Alireza Akbari's hanging was reported by Iranian state media on Saturday.
A few hours before that, the United States had urged Iran not to go ahead with the execution.
Convicted of espionage
"We mourn with his loved ones and will continue to hold Iran accountable for its sham trials and politicized executions," US Secretary of State Antony Blinken wrote on Twitter.
France has also reacted strongly, pledging a response to Iran's repeated violations of international law, particularly when it comes to executions of arbitrarily detained foreign nationals.
Akbari, who was Iran's deputy defense minister, was arrested in 2019 and convicted of spying for Britain, which he denies.