HMS Dasher exploded off Arran in March, 1943, killing 379 people, but only 23 bodies are in marked graves across Scotland. The other bodies have never been accounted for.
John Steele, a writer from Ardrossan whose one-man campaign has led to the search, believes some of the bodies were buried in an unmarked grave at the town's cemetery in a cover-up by the British Admiralty.
Mr Steele says there was a fatal flaw in the design of the American-built HMS Dasher but the British authorities did not want it made public for fear of upsetting their wartime ally.
Permission has now been given for excavation work to be carried out at Ardrossan Cemetery to establish if some of the Dasher victims are buried there.
North Ayrshire Council submitted a petition to Kilmarnock Sheriff Court seeking permission to carry out excavation in the cemetery. The petition has been granted, which means archaeologists can now go ahead with the work.
Mr Steele said he hoped the excavation would finally clear up the mystery of where many of the bodies ended up. Sixty bodies were taken ashore at Ardrossan, meaning there could be around 44 bodies in the mass grave.
"It's wrong that young men who fought for their country and gave up their lives should be treated in this way," he said.
"There was a cover-up because the Americans had made a grave mistake in the design of the petrol storage system on the Dasher which resulted in numerous leaks."
One person who supports the excavation is Eunice Clarke, whose father George Wood was a fireman on the Dasher. The whereabouts of Mr Wood's body is unknown.
Mrs Clarke, 72, of Bridge of Weir, said: "We don't know what happened to my father or where his body is. I would like the excavation to go ahead so we can find out. My mother died not knowing. Growing up, I began to realise what she went through and it's upsetting for me not to know."
Mr Steele says evidence he uncovered for his book about the disaster, The American Connection To The Sinking of HMS Dasher, shows the captain of the vessel had warned there was a serious fault with the fuel system but nothing was done.
"The Admirality took a gamble," said Mr Steele, "but they lost the gamble, which cost us a valuable aircraft carrier and 379 lives."
Dasher, which had 24 Scots among its crew, blew up on March 27, 1943, five miles off Cumbrae. The families were all told their relatives were posted dead or missing but they were not told the details of what happened.
Mr Steele believes some of the bodies that were taken ashore were buried anonymously at Ardrossan Cemetery as part of the cover-up. He identified a disused plot at the cemetery where he believes the bodies may be.
Initial investigations by Tony Pollard, an archaeologist at Glasgow University, suggested there might be bodies at the site. Mr Pollard recommended a search, which will now be carried out by the Glasgow archaeology firm Guard.
Mr Steele said the search was a big step forward in his campaign to reopen the case of the Dasher.
"If the bodies are there, all I want is a plaque up, we can have a service and give them some dignity," he said. "To think that they are in there without coffins, they have been dumped. I'm angry it should have been covered up all these years and mothers and fathers died of broken hearts never to be told the truth because the Admirality made a decision that it was war time, we have a wonderful ally in America, we can't upset them, we can't upset the public.
"Even today, it's disgraceful this is still a secret. It's shocking."
A spokesman for North Ayrshire Council said: "The council understands the sensitivities surrounding this matter, both for the relatives of those who died and the need to maintain the sanctity of the cemetery itself.
"We submitted a petition to Kilmarnock Sheriff Court seeking permission to carry out limited excavation in Ardrossan Cemetery.
"This petition was successful and the archaeologists have been given the go-ahead to carry this work out. There are a number of conditions attached to ensure the work is carried out appropriately and with minimum disruption to the cemetery."