After a short hearing, Michael Burgess, Surrey county coroner, adjourned the inquest until a date to be determined later.
Police said on Thursday that detailed toxicological tests were under way but would take several weeks to complete.
Once the tests were finished, the body will be returned to Georgia, the Patarkatsishvili family said in a statement.
"We thank everybody who shares our grief. We completely trust the professionalism of the British police and criminal experts," the statement said.
Patarkatsishvili was at his home in Leatherhead, Surrey, with his family when he complained of chest pains, said Camille Juliff, coroner's officer.
He went upstairs where he collapsed, and was pronounced dead at 2252 GMT.
The court was told there was no evidence of any radioactive substance in his body.
The suspicion of radioactive poisoning was raised because of the death of Alexander Litvinenko, a former KGB agent, in Britain in 2006.
Litvinenko was poisoned with radioactive Isotope Polonium-210.
Patarkatsishvili had built his fortune in Russia after the break-up of the Soviet Union through a partnership with Boris Berezovsky.
Berezovsky is a Russian businessman and one of the most vocal foes of Vladimir Putin, the Russian president.
Campaigning from Britain, Patarkatsishvili ran for president last month, losing to the incumbent, Mikhail Saakashvili.
Opposition groups say the vote was rigged.
Patarkatsishvili helped lead anti-government protests in November and was under investigation at home on charges of plotting to overthrow the government.
He denied the accusations, but acknowledged offering a senior police official $100 million if police agreed not to respond with force during street protests after the January election.
The Georgian opposition has called for a mass protest on the streets of Tbilisi, Georgia's capital, and boycott of parliament on Friday unless authorities carry out a recount of the presidential vote.