The animals were discovered inside an item of luggage by officers carrying out customs checks at the airports Terminal 5 on Monday 3 February.
Each was wrapped in an individual sock. Twelve survived their journey, one had died in transit.
The San Salvador Rock Iguanas are controlled under the Convention on International Trade in Endangered Species (CITES) and so were seized.
Two people were arrested on suspicion of importation offences, Romanian women aged 24 and 26. They had arrived on a flight from the Bahamas and were due to fly on to Dusseldorf in Germany.
Officers from the National Crime Agencys Border Policing Command are now investigating.
Grant Miller, head of the Border Force CITES team, said:
This particular species of iguana is incredibly rare only a few hundred are believed to be left in existence so this was a remarkable and very important seizure.
Given the circumstances we found them in it seems incredible that all but one survived such a long flight.
The surviving animals were dehydrated and are now under the supervision of a specialist vet. We are also working with experts to find the best way to protect and safeguard these endangered creatures longer term.
Border Force is responsible for frontline detection and seizure duties on the illegal trade in endangered animals and plants which is covered by the CITES convention. The convention covers more than 35,000 species of animals and plants, whether they are traded as live specimens or as derivatives.
The Heathrow-based Border Force CITES team are specialist officers who work closely with the National Wildlife Crime Unit (NWCU), NCA and police to provide expert advice on border operational issues. They are recognised as world leaders in their field, most recently by the World Customs Organisation at their annual international customs day.
In the year 2012/13 Border Force Officers made more than 690 seizures under CITES regulations, up from 516 the year before. Among them were 326 ivory items and 93 live animals.
Anyone with information about activity they suspect may be linked to smuggling should call our hotline on 0800 59 5000.