Police launched a fresh search on the island amid claims Konstantinos Barkas, also known as Dino, may have been responsible for Ben's death as he was clearing land with an excavator near the spot where the child had been playing on the day he vanished.
Mr Barkas is believed to have died from stomach cancer last year and South Yorkshire Police has now formally ended its latest search.
Extensive searches of a fly-tipping site uncovered a yellow toy car police believe the toddler had at the time he disappeared.
Shortly after the revelation earlier this month, Ben's grandmother Christine told the Daily Mirror she remembered buying him two toy cars in Kos town centre.
The 64-year-old said: 'I was shaken by it and both me and Kerry (Ben's mother) cried. I just felt sick really. It was a shock. I expected it to have no paint on but I was 90% sure it was Ben's. When I saw it I felt disbelief.'
Referring to digger driver Konstantinos Barkas, also known as Dino, she said: 'It must have been dumped at that site by Dino. It didn't walk there.'
Ben, from Sheffield, disappeared on July 24, 1991, aged 21 months, after travelling to the island with his mother and grandparents.
The events charting the disappearance of Sheffield toddler Ben Needham on the Greek island of Kos 25 years ago
July 24 1991: Ben Needham vanishes while playing near the grounds of a farmhouse in the Iraklis region of Kos, which his family are renovating. His mother, Kerry Needham, and grandparents raise the alarm with local police and conduct a full search of the area.
July 26 1991: Eyewitness reports claim a boy matching Ben's description was found at the local airport on the day he disappeared. That boy has never been traced.
September 1991: The Needham family return to England due to illness, but vow to continue the search.
June 2003: The Metropolitan Police issue an image of what Ben might look like at age 12-14 years old.
2004: An anonymous businessman offers a reward of £500,000 for information leading to Ben's safe return.
October 2010: Another public appeal is made by Ben's mother in the run-up to what would be his 21st birthday.
May 2011: The BBC airs a programme called Missing 2011, which includes a piece on Ben's story and the campaign to find him.
September 2011: Greek police on Kos officially re-open the case and grant the family a face-to-face meeting with the island's prosecutor.
October 2012: South Yorkshire Police in Kos begin digging up mounds around the property where Ben went missing to look for his remains.
December 2013: Ben's mother accuses then-prime minister David Cameron of not giving her case the same backing as he gave the parents of Madeline McCann. It comes as a dossier is produced containing reports from eight witnesses, none of who know each other, who all saw a boy possibly matching Ben's description with the same Greek family.
December 2014: Lawyers representing Ben's family say they may take legal action to try to force the Government to make a decision about funding a new police investigation.
January 2015: The Home Office agrees to fund a team of British detectives to help search for the toddler.
March/April 2015: Three generations of Ben Needham's family travel to Greece to follow up a 'strong' lead that a man living there believes he may be the missing Brit due to having no photographs of himself under the age of two and no knowledge of where he was born. The man is later ruled out.
May 2015: Ben's family make a fresh appeal on Greek television for information regarding the disappearance.
May 2016: The Sun newspaper publishes a report that members of the police operation go on an 'eight-hour booze-up' in Kos during the latest stage of the investigation.
September 2016: Ben's family are told to 'prepare for the worst' by detectives leading the investigation, amid the belief the 21-month-old was crushed to death by a digger - the driver of which died in 2015. It comes as police arrive in Kos to begin excavation work in the belief the boy's remains may be buried near the farmhouse
October 16 2016: Officers formally end a three-week search of two sites on Kos. Detectives said they had accumulated more than 60 items of interest that would be brought back to the UK for forensic testing.
October 17 2016: South Yorkshire Police announces that it believes Ben died as a result of an accident near to the farmhouse where he disappeared.
