Surrey resident Pat Harrington launched the petition last year following the death of her son Ben (32) in 2012.
She does not accept the official explanation by the Thai police that her son died after his motorbike crashed into an electricity pylon. More than 13,000 people signed the Change.org petition, which was given to the UK government last week.
Mrs Harrington spent years trying to get information from the Thai authorities about her son’s death, including submitting freedom of information requests to the Foreign and Commonwealth Office.
She also said that she had to fight to stop her son’s body being cremated the day after his death.
Koh Tao – a party island popular with backpackers – has come under scrutiny in recent years following a number of suspicious or unexplained deaths.
Among them are the murders of former Victoria College student Mr Miller (24) and UK resident Hannah Witheridge, who were beaten to death on a beach in the island.
Two Burmese migrants, who say they were tortured into confessing, were later convicted of the crimes, but some international human rights observers claim they were victims of a miscarriage of justice.
In a statement following the convictions, Mr Miller’s family said they believed the police investigation had been ‘methodical and thorough’ and that justice had been done.
In a statement accompanying the petition, Mrs Harrington says: ‘The British government need to take notice of what is happening to our children on this island and do something regarding further investigations into their deaths. Theresa May, this needs to be looked into NOW before any more lives are taken.’