The items mostly dated from between 2100BC and 1800BC, originating from the third Ur dynasty or Old Babylonian dynasty, according to The Times.
They were impounded at a freight forwarder near Heathrow Airport in 2011 when customs officials seized a shipment headed to Britain from the United Arab Emirates (UAE).
Declared as "miniature handmade clay tiles", the shipment was declared to have a value of a few hundred pounds.
The haul, which could have fetched tens of thousands of pounds on the black market, is believed to have been looted in 2003 in the months following the US-led invasion of Iraq, and smuggled out through the UAE.
Experts believe looters might have "hit the jackpot" when digging at the site of an ancient city in what is now southern Iraq called Irisagrig, the paper reported.
More than 15,000 items were looted from Iraq's National Museum, in Baghdad, following the US invasion, of which some 8,000 have been returned.
All such artefacts which are intercepted by police are handed to the British Museum for examination.
An investigation into the smuggling attempt was continuing, police said.