Six Caribbean LGBTQ+ organisations have entered submissions supporting his case.
The laws date back to the reign of Henry VIII, when a medieval ecclesiastical law was passed after the break with Rome into civil law, making "the detestable and abominable vice of buggery" subject to the death penalty.
Britain abolished the law in 1967 and has since pardoned gay men prosecuted under it. But it remains in place in many former British territories.
Jones began his case against his country incensed by broken promises to tackle homophobia at the 2015 Commonwealth heads of government meeting.
He had the backing of the late Jonathan Cooper, a former colleague of Keir Starmer, whose Human Dignity Trust set the ball rolling.
"I'm nothing special. I dropped out of college.
I survived HIV. All I am is a very angry gay man.
I think about all the friends and lovers I've lost over the last 40 years. This is a dream we couldn't dream back then," Jones said.
Legal Nuances and Historical Irony
The final decision will rest with a panel of five judges, including outgoing Supreme Court President Lord Reed, and will hinge upon interpretations of savings law clauses that carried over existing British laws into newly independent states, such as Trinidad and Tobago in 1962, to facilitate smooth transition of judicial sovereignty.
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Jones's case argues that since British laws against sodomy were repealed by Trinidad in 1986 and replaced with new and harsher laws, including extending the prohibition of anal sex to women, the savings law clause protections cannot apply.
