In a statement to the House of Commons, Treasury minister Sarah McCarthy-Fry said the measure was taken because Bank Mellat had provided services to an organisation "connected to Iran's proliferation-sensitive activities."
It had also been "involved in transactions related to financing Iran's nuclear and ballistic missile programme," she said.
The shipping firm had "transported goods for both Iran's ballistic missile and nuclear programmes," she added.
"Financial and credit institutions will no longer be able to enter into new transactions or business relationships with these entities, nor to continue with existing transactions or business relationships unless they are licensed by HM Treasury," McCarthy-Fry said in a written statement.
Western powers suspect Iran's nuclear programme is aimed at making atomic weapons, a charge strongly denied by Tehran.
World powers including Britain were outraged when Iran revealed last month that it was building a second uranium enrichment plant near the holy city of Qom.
But a Treasury spokesman said Monday's announcement was not connected to the latest developments in the stand-off.
The next stage in six-party talks on Iran's nuclear programme comes on October 19.
Officials from Iran, the United States, Russia, France and the International Atomic Energy Agency (IAEA) will meet in Vienna to work out the deals under which Tehran has said it is ready to buy 20 percent pure uranium from abroad.